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Finding the Slope of a Graph In Exercises \(25-32,\) find \(d y / d x\) by implicit differentiation. Then find the slope of the graph at the given point. \(3 x^{3} y=6, \quad(1,2)\)

Finding a Derivative In Exercises 7-26, use the rules of differentiation to find the derivative of the function. $$ y=7 x^{4}+2 \sin x$$

Finding the Derivative by the Limit Process In Exercises 15-28, find the derivative of the function by the limit process. $$f(x)=\frac{1}{x^{2}}$$

Finding the Slope of a Graph In Exercises \(25-32,\) find \(d y / d x\) by implicit differentiation. Then find the slope of the graph at the given point. \(y^{2}=\frac{x^{2}-49}{x^{2}+49}, \quad(7,0)\)

Finding a Derivative IIn Exercises \(9-34,\) find the derivative of the function. \(y=\frac{x}{\sqrt{x^{2}+1}}\)

Finding the Derivative by the Limit Process In Exercises 15-28, find the derivative of the function by the limit process. $$f(x)=\sqrt{x+4}$$

Finding a Derivative IIn Exercises \(9-34,\) find the derivative of the function. \(y=\frac{x}{\sqrt{x^{4}+4}}\)

Finding the Slope of a Graph In Exercises \(25-32,\) find \(d y / d x\) by implicit differentiation. Then find the slope of the graph at the given point. \(4 y^{3}=\frac{x^{2}-36}{x^{3}+36},(6,0)\)

Finding the Derivative by the Limit Process In Exercises 15-28, find the derivative of the function by the limit process. $$h(s)=-2 \sqrt{s}$$

Finding the Slope of a Graph In Exercises \(25-32,\) find \(d y / d x\) by implicit differentiation. Then find the slope of the graph at the given point. \((x+y)^{3}=x^{3}+y^{3}, \quad(-1,1)\)