91Ó°ÊÓ

Calculate the derivatives of the functions in Exercises 1-46. HINT [See Example 1.] \(r(x)=\left(0.1 x^{2}-4.2 x+9.5\right)^{1.5}\)

Find the derivative of each function. HINT [See Examples 1 and 2.] $$ g(x)=x^{-2}-3 x^{-1}-2 $$

The daily cost to manufacture generic trinkets for gullible tourists is given by the cost function $$ C(x)=-0.001 x^{2}+0.3 x+500 \text { dollars } $$ where \(x\) is the number of trinkets. a. As \(x\) increases, the marginal cost \(\begin{array}{lll}\text { (A) increases } & \text { (B) decreases } & \text { (C) increases, then }\end{array}\) decreases (D) decreases, then increases b. As \(x\) increases, the average cost (A) increases (B) decreases (C) increases, then decreases (D) decreases, then increases c. The marginal cost is \(\begin{array}{lll}\text { (A) greater than } & \text { (B) equal to } & \text { (C) less than }\end{array}\) the average cost when \(x=100\). HINT [See Example 4.]

Calculate \(\frac{d y}{d x}\) in Exercises 21-50. You need not expand your answers. \(y=(x+1)\left(x^{2}-1\right)\)

Calculate the derivatives of the functions in Exercises 1-46. HINT [See Example 1.] \(r(x)=\left(0.1 x-4.2 x^{-1}\right)^{0.5}\)

Calculate \(\frac{d y}{d x}\) in Exercises 21-50. You need not expand your answers. \(y=\left(4 x^{2}+x\right)\left(x-x^{2}\right)\)

Find the derivative of each function. HINT [See Examples 1 and 2.] $$ g(x)=2 x^{-1}+4 x^{-2} $$

Calculate the derivatives of the functions in Exercises 1-46. HINT [See Example 1.] \(r(s)=\left(s^{2}-s^{0.5}\right)^{4}\)

Find the derivative of each function. HINT [See Examples 1 and 2.] $$ g(x)=\frac{1}{x}-\frac{1}{x^{2}} $$

Calculate \(\frac{d y}{d x}\) in Exercises 21-50. You need not expand your answers. \(y=\left(2 x^{0.5}+4 x-5\right)\left(x-x^{-1}\right)\)