91Ó°ÊÓ

Use logarithmic differentiation to find the derivative of the function. Find \(y^{\prime \prime}\) if \(y=x^{x}\).

Unclogging Arteries Research done in the 1930 s by the French physiologist Jean Poiseuille showed that the resistance \(R\) of a blood vessel of length \(l\) and radius \(r\) is \(R=k l / r^{4}\), where \(k\) is a constant. Suppose that a dose of the drug TPA increases \(r\) by \(10 \% .\) How will this affect the resistance \(R\) ? (Assume that \(I\) is constant.)

Acceleration of a Car A car starting from rest and traveling in a straight line attains a velocity of $$v(t)=\frac{110 t}{2 t+5}$$ feet per second after \(t\) sec. Find the initial acceleration of the car and its acceleration \(10 \mathrm{sec}\) after starting from rest.

Find the derivative of the function and \(\underline{\text { eval }}\) uate \(f^{\prime}(x)\) at the given value of \(x\). \(f(x)=(\sqrt{x}+2 x)\left(x^{3 / 2}-x\right) ; \quad x=4\)

Find the derivative of the function. Let \(f(x)=2 x^{3}-4 x\), Find a. \(f^{\prime}(-2)\) b. \(f^{\prime}(0)\) c. \(f^{\prime}(2)\)

The weekly total cost in dollars incurred by the BMC Recording Company in manufacturing \(x\) compact discs is $$C(x)=4000+3 x-0.0001 x^{2} \quad 0 \leq x \leq 10,000$$ a. What is the actual cost incurred by the company in producing the 2001 st disc? The 3001 st disc? b. What is the marginal cost when \(x=2000\) ? When \(x=3000 ?\)

Use logarithmic differentiation to find the derivative of the function. Find \(y^{\prime}\) if \(y=x^{x^{x}}\).

Find the derivative of the function. $$ f(x)=\tan ^{2} x+\cot x^{2} $$

Sketch the graph of the derivative \(f^{\prime}\) of the function \(f\) whose graph is given.

Let \(f(x)=4 x^{5 / 4}+2 x^{3 / 2}+x\). Find a. \(f^{\prime}(0)\) b. \(f^{\prime}(16)\)