91Ó°ÊÓ

Finding a Derivative In Exercises \(29-40\) , find the derivative of the alvebraic function. \(g(s)=s^{3}\left(5-\frac{s}{s+2}\right)\)

Electricity The combined electrical resistance \(R\) of two resistors \(R_{1}\) and \(R_{2},\) connected in parallel, is given by \(\frac{1}{R}=\frac{1}{R_{1}}+\frac{1}{R_{2}}\) where \(R, R_{1},\) and \(R_{2}\) are measured in ohms. \(R_{1}\) and \(R_{2}\) are increasing at rates of 1 and 1.5 ohms per second, respectively. At what rate is \(R\) changing when \(R_{1}=50\) ohms and \(R_{2}=75\) ohms?

Finding a Derivative of a Trigonometric Function In Exercises \(35-54\) , find the derivative of the trigonometric function. $$g(x)=5 \tan 3 x$$

Finding the Slope of a Graph In Exercises \(31-38\) , find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. $$g(t)=-2 \cos t+5$$ $$(\pi, 7)$$

Electrical Circuit The voltage \(V\) in volts of an electrical circuit is \(V=I R,\) where \(R\) is the resistance in ohms and I is the current in amperes. \(R\) is increasing at a rate of 2 ohms per second, and \(V\) is increasing at a rate of 3 volts per second. At what rate is \(I\) changing when \(V=12\) volts and \(R=4\) ohms?

Finding a Derivative of a Trigonometric Function In Exercises \(35-54\) , find the derivative of the trigonometric function. $$h(x)=\sec 6 x$$

Finding a Derivative In Exercises \(29-40\) , find the derivative of the alvebraic function. \(g(x)=x^{2}\left(\frac{2}{x}-\frac{1}{x+1}\right)\)

Finding a Derivative In Exercises \(39-54,\) find the derivative of the function. $$f(x)=x^{2}+5-3 x^{-2}$$

Finding a Derivative of a Trigonometric Function In Exercises \(35-54\) , find the derivative of the trigonometric function. $$y=\sin (\pi x)^{2}$$

Finding a Derivative In Exercises \(29-40\) , find the derivative of the alvebraic function. \(f(x)=\left(2 x^{3}+5 x\right)(x-3)(x+2)\)