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Problem 10

Calculate the derivatives of the functions in Exercises 1-46. HINT [See Example 1.] \(f(x)=(x+7)^{-2}\)

Expert verified

The derivative of the function \(f(x) = (x+7)^{-2}\) is \(f'(x) = -2(x+7)^{-3}\).

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Chapter 11

Calculate the derivatives of the functions in Exercises 1-46. HINT [See Example 1.] \(g(x)=\left(x^{2}-3 x-1\right)^{-5}\)

Chapter 11

Calculate the derivatives of the functions in Exercises 1-46. HINT [See Example 1.] \(r(s)=\left(2 s+s^{0.5}\right)^{-1}\)

Chapter 11

Calculate the derivatives of the functions in Exercises 1-46. HINT [See Example 1.] \(f(x)=(1-x)^{-1}\)

Chapter 11

Compute the indicated derivative using the chain rule. HINT [See Quick Examples on page 828.] \(x=1-t / 2, y=4 t-1 ; \frac{d y}{d x}\)

Chapter 11

Find the equation of the line tangent to the graph of the given function at the point with the indicated \(x\) -coordinate. \(f(x)=\frac{x+1}{x+2} ; x=0\)

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