Find \( y^{\prime} \) given \( y=x^{2} \cos x \)

Use a calculator to evaluate the expression. \( \frac{\ln 9+\ln 3}{\log 9+\log 3} \) \( \frac{\ln 9+\ln 3}{\log 9+\log 3} \approx \square \)

Differentiate. \( f(x)=\sqrt{11 x-x^{3}} \) 1

\( \int _{}^{}\cot (x)^{3}\csc (x)^{2} d \)

A business estimates that the salvage value V of a piece of machinery after t years is given by, \( \mathrm{V}(\mathrm{t})=\$ 34,000 e^{-0.4 \mathrm{t}} \). After what amount of time will the salvage value be \( \$ 1986 \) ?

Encuentre la pendiente de la recta tangente a la curva \( y=f(x) \) en el punto \( (1,1 / 4) \) \( y=f(x)=\frac{2 x-x^{2}}{1+3 x} \) Seleccione una: a. \( -3 / 4 \) b. -4 c. -3 d. \( -3 / 16 \)