Functions-Derivatives-Integrals Calculator

Function1st Derivative2nd DerivativeIntegralSimpsons Rule
Evaluate at ƒ()Evaluate at ƒ'()Evaluate at ƒ''()Evaluate at Evaluate at
n =

Given the equation ƒ(a) = a2 - a + 6, determine the 1st derivative ƒ'(a)

Using the power rule, the derivative ƒ'(a) of aan = (a * n)a(n - 1)
For this term, a = 1, n = 2, and a is the variable we derive in terms of
ƒ(a) = a2
ƒ'(a) = (1 * 2)a(2 - 1)
ƒ'(a) = 2a <--- Used in our final answer.

Using the power rule, the derivative ƒ'(a) of aan = (a * n)a(n - 1)
For this term, a = -1, n = 1, and a is the variable we derive in terms of
ƒ(a) = -a
ƒ'(a) = (-1 * 1)a(1 - 1)
ƒ'(a) = -1 <--- Used in our final answer.

Using the power rule, the derivative ƒ'(a) of aan = (a * n)a(n - 1)
For this term, a = 6, n = 0, and a is the variable we derive in terms of
ƒ(a) = 6
ƒ'(a) = 0 <--- The derivative of a constant = 0. This is part of our answer.

Collecting all of our derivative terms we get:
ƒ'(a) = 2a - 1

Evaluate ƒ'(0)
ƒ'(0) = 2(0) - 1
ƒ'(0) = 2(0) - 1
ƒ'(0) = 0 - 1
ƒ'(0) = -1