Problem 1
Each edge of a variable cube is increasing at a rate of 3 inches per second. How fast is the volume of the cube increasing when an edge is 12 inches long?
Problem 1
Find \(D_{x} y\). $$ y=(1+x)^{15} $$
Problem 1
Assuming that each equation defines a differentiable function of \(x\), find \(D_{x} y\) by implicit differentiation. \(y^{2}-x^{2}=1\)
Problem 1
Find \(d^{3} y / d x^{3}\). $$ y=x^{3}+3 x^{2}+6 x $$
Problem 1
In Problems 1-44, find \(D_{x} y\) using the rules of this section. $$ y=2 x^{2} $$
Problem 1
Find \(D_{x} y\). $$ y=\sinh ^{2} x $$
Problem 1
1-6, show that \(f\) has an inverse by showing that it is strictly monotonic. $$ f(x)=-x^{5}-x^{3}-x $$
Problem 1
$$ \text { } \text { find } D_{x} y . $$ $$ y=2 \sin x+3 \cos x $$
Problem 1
Find \(d y\). $$ y=x^{2}+x-3 $$
Problem 1
Use the definition $$f^{\prime}(c)=\lim _{h \rightarrow 0} \frac{f(c+h)-f(c)}{h}$$ to find the indicated derivative. $$ f^{\prime}(1) \text { if } f(x)=x^{2} $$
