Studdy AI Logo
Math

QuestionFind the derivative of the function f(x)=2x−10+7x−2f(x)=2 x^{-10}+7 x^{-2}. What is f′(x)f^{\prime}(x)?

Studdy Solution

STEP 1

Assumptions1. The function is f(x)=x−10+7x−f(x)= x^{-10}+7 x^{-} . We need to find the derivative of the function f(x)f(x), denoted as f′(x)f'(x)

STEP 2

To find the derivative of f(x)f(x), we need to apply the power rule. The power rule states that the derivative of xnx^n is nxn−1nx^{n-1}.

STEP 3

Apply the power rule to the first term 2x−102x^{-10}.
ddx(2x−10)=−10⋅2x−10−1\frac{d}{dx}(2x^{-10}) = -10 \cdot2x^{-10-1}

STEP 4

implify the derivative of the first term.
ddx(2x−10)=−20x−11\frac{d}{dx}(2x^{-10}) = -20x^{-11}

STEP 5

Apply the power rule to the second term 7x−27x^{-2}.
ddx(7x−2)=−2⋅7x−2−1\frac{d}{dx}(7x^{-2}) = -2 \cdot7x^{-2-1}

STEP 6

implify the derivative of the second term.
ddx(x−2)=−14x−3\frac{d}{dx}(x^{-2}) = -14x^{-3}

STEP 7

Combine the derivatives of the two terms to get the derivative of the function f(x)f(x).
f′(x)=ddx(2x−10)+ddx(7x−2)f'(x) = \frac{d}{dx}(2x^{-10}) + \frac{d}{dx}(7x^{-2})

STEP 8

Substitute the derivatives of the two terms into the equation.
f′(x)=−20x−11−14x−3f'(x) = -20x^{-11} -14x^{-3}So, the derivative of the function f(x)=2x−10+7x−2f(x) =2x^{-10} +7x^{-2} is f′(x)=−20x−11−14x−3f'(x) = -20x^{-11} -14x^{-3}.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord