Given ƒ(x) = 3x4 + 6x3 - 123x2 - 126x + 1080
Determine the 2nd derivative ƒ''(x)
Start ƒ''(x)
Use the power rule
ƒ''(x) of axn = (a * n)x(n - 1)For this term, a = 3, n = 4
and x is the variable we derive
ƒ''(x) = 3x4
ƒ''(x)( = 3 * 4)x(4 - 1)
ƒ''(x) = 12x3
Use the power rule
ƒ''(x) of axn = (a * n)x(n - 1)For this term, a = 6, n = 3
and x is the variable we derive
ƒ''(x) = 6x3
ƒ''(x)( = 6 * 3)x(3 - 1)
ƒ''(x) = 18x2
Use the power rule
ƒ''(x) of axn = (a * n)x(n - 1)For this term, a = -123, n = 2
and x is the variable we derive
ƒ''(x) = -123x2
ƒ''(x)( = -123 * 2)x(2 - 1)
ƒ''(x) = -246x
Use the power rule
ƒ''(x) of axn = (a * n)x(n - 1)For this term, a = -126, n = 1
and x is the variable we derive
ƒ''(x) = -126x
ƒ''(x)( = -126 * 1)x(1 - 1)
ƒ''(x) = -126
Use the power rule
ƒ''(x) of axn = (a * n)x(n - 1)For this term, a = 1080, n = 0
and x is the variable we derive
ƒ''(x) = 1080
ƒ''(x) = 0 <--- The derivative of a constant = 0. This is part of our answer.
Collecting all of our derivative terms
ƒ''(x) = 12x3 + 18x2 - 246x - 126Start ƒ''(x)
Use the power rule
ƒ''(x) of axn = (a * n)x(n - 1)For this term, a = 3, n = 4
and x is the variable we derive
ƒ''(x) = 3x4
ƒ''(x)( = 3 * 4)x(4 - 1)
ƒ''(x) = 12x3
Use the power rule
ƒ''(x) of axn = (a * n)x(n - 1)For this term, a = 6, n = 3
and x is the variable we derive
ƒ''(x) = 6x3
ƒ''(x)( = 6 * 3)x(3 - 1)
ƒ''(x) = 18x2
Use the power rule
ƒ''(x) of axn = (a * n)x(n - 1)For this term, a = -123, n = 2
and x is the variable we derive
ƒ''(x) = -123x2
ƒ''(x)( = -123 * 2)x(2 - 1)
ƒ''(x) = -246x
Use the power rule
ƒ''(x) of axn = (a * n)x(n - 1)For this term, a = -126, n = 1
and x is the variable we derive
ƒ''(x) = -126x
ƒ''(x)( = -126 * 1)x(1 - 1)
ƒ''(x) = -126
Use the power rule
ƒ''(x) of axn = (a * n)x(n - 1)For this term, a = 1080, n = 0
and x is the variable we derive
ƒ''(x) = 1080
ƒ''(x) = 0 <--- The derivative of a constant = 0. This is part of our answer.
Collecting all of our derivative terms
ƒ''(x) = 12x3 + 18x2 - 246x - 126Start ƒ''(x)
Use the power rule
ƒ''(x) of axn = (a * n)x(n - 1)For this term, a = 3, n = 4
and x is the variable we derive
ƒ''(x) = 3x4
ƒ''(x)( = 3 * 4)x(4 - 1)
ƒ''(x) = 12x3
Use the power rule
ƒ''(x) of axn = (a * n)x(n - 1)For this term, a = 6, n = 3
and x is the variable we derive
ƒ''(x) = 6x3
ƒ''(x)( = 6 * 3)x(3 - 1)
ƒ''(x) = 18x2
Use the power rule
ƒ''(x) of axn = (a * n)x(n - 1)For this term, a = -123, n = 2
and x is the variable we derive
ƒ''(x) = -123x2
ƒ''(x)( = -123 * 2)x(2 - 1)
ƒ''(x) = -246x
Use the power rule
ƒ''(x) of axn = (a * n)x(n - 1)For this term, a = -126, n = 1
and x is the variable we derive
ƒ''(x) = -126x
ƒ''(x)( = -126 * 1)x(1 - 1)
ƒ''(x) = -126
Use the power rule
ƒ''(x) of axn = (a * n)x(n - 1)For this term, a = 1080, n = 0
and x is the variable we derive
ƒ''(x) = 1080
ƒ''(x) = 0 <--- The derivative of a constant = 0. This is part of our answer.
Collecting all of our derivative terms
ƒ''(x) = 12x3 + 18x2 - 246x - 126Start ƒ''(x)
Use the power rule
ƒ''(x) of axn = (a * n)x(n - 1)For this term, a = 3, n = 4
and x is the variable we derive
ƒ''(x) = 3x4
ƒ''(x)( = 3 * 4)x(4 - 1)
ƒ''(x) = 12x3
Use the power rule
ƒ''(x) of axn = (a * n)x(n - 1)For this term, a = 6, n = 3
and x is the variable we derive
ƒ''(x) = 6x3
ƒ''(x)( = 6 * 3)x(3 - 1)
ƒ''(x) = 18x2
Use the power rule
ƒ''(x) of axn = (a * n)x(n - 1)For this term, a = -123, n = 2
and x is the variable we derive
ƒ''(x) = -123x2
ƒ''(x)( = -123 * 2)x(2 - 1)
ƒ''(x) = -246x
Use the power rule
ƒ''(x) of axn = (a * n)x(n - 1)For this term, a = -126, n = 1
and x is the variable we derive
ƒ''(x) = -126x
ƒ''(x)( = -126 * 1)x(1 - 1)
ƒ''(x) = -126
Use the power rule
ƒ''(x) of axn = (a * n)x(n - 1)For this term, a = 1080, n = 0
and x is the variable we derive
ƒ''(x) = 1080
ƒ''(x) = 0 <--- The derivative of a constant = 0. This is part of our answer.
Collecting all of our derivative terms
ƒ''(x) = 12x3 + 18x2 - 246x - 126Evaluate ƒ''(0)
ƒ''(0) = 12(0)3 + 18(0)2 - 246(0) - 126ƒ''(0) = 12(0) + 18(0) - 246(0) - 126
ƒ''(0) = 0 + 0 + 0 - 126
Final Answer
ƒ''(0) = -126
You have 2 free calculationss remaining
What is the Answer?
ƒ''(0) = -126
How does the Functions-Derivatives-Integrals Calculator work?
Free Functions-Derivatives-Integrals Calculator - Given a polynomial expression, this calculator evaluates the following items:
1) Functions ƒ(x). Your expression will also be evaluated at a point, i.e., ƒ(1)
2) 1st Derivative ƒ‘(x) The derivative of your expression will also be evaluated at a point, i.e., ƒ‘(1)
3) 2nd Derivative ƒ‘‘(x) The second derivative of your expression will be also evaluated at a point, i.e., ƒ‘‘(1)
4) Integrals ∫ƒ(x) The integral of your expression will also be evaluated on an interval, i.e., [0,1]
5) Using Simpsons Rule, the calculator will estimate the value of ≈ ∫ƒ(x) over an interval, i.e., [0,1]
This calculator has 7 inputs.
1) Functions ƒ(x). Your expression will also be evaluated at a point, i.e., ƒ(1)
2) 1st Derivative ƒ‘(x) The derivative of your expression will also be evaluated at a point, i.e., ƒ‘(1)
3) 2nd Derivative ƒ‘‘(x) The second derivative of your expression will be also evaluated at a point, i.e., ƒ‘‘(1)
4) Integrals ∫ƒ(x) The integral of your expression will also be evaluated on an interval, i.e., [0,1]
5) Using Simpsons Rule, the calculator will estimate the value of ≈ ∫ƒ(x) over an interval, i.e., [0,1]
This calculator has 7 inputs.
What 1 formula is used for the Functions-Derivatives-Integrals Calculator?
What 8 concepts are covered in the Functions-Derivatives-Integrals Calculator?
- derivative
- rate at which the value y of the function changes with respect to the change of the variable x
- exponent
- The power to raise a number
- function
- relation between a set of inputs and permissible outputs
ƒ(x) - functions-derivatives-integrals
- integral
- a mathematical object that can be interpreted as an area or a generalization of area
- point
- an exact location in the space, and has no length, width, or thickness
- polynomial
- an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).
- power
- how many times to use the number in a multiplication
Example calculations for the Functions-Derivatives-Integrals Calculator
Tags:
Add This Calculator To Your Website
