Which function $f\left(x\right)$ and value $a$ correspond to the following limit representing the derivative of $f$ at $a$?$$\underset{h\to 0}{lim}\frac{{(3+h)}^2-9}{h}$$

Given $y=x\ln \left(x\right)$, which of the following correctly gives both the first and second derivatives, $y^{\prime }$ and $y^{″}$?

Given the function $f\left(x\right)=\sin \left(x\right)\ln \left(x^4\right)$, compute $f^{\prime }\left(x\right)$. Which of the following is correct?

Given the function $f(x,y)=ax+by+cx+dy$, where $a$, $b$, $c$, and $d$ are constants, find the first partial derivatives $f_x$ and $f_y$.

Find the derivative of the function $h\left(x\right)=x^2\sin \left(x\right)$. Which of the following is correct?

Which of the following best describes the derivative of a function $f$ at a point $x=a$?

Given $f(x,y)={\sin }^2(mx+ny)$, which of the following is the correct expression for the second mixed partial derivative $\frac{{\partial }^{2}f}{\partial x\partial y}$?

Find the derivative of the function: $y=arctan\frac{1+x}{1-x}$. Which of the following is correct?

Find the derivative of the function: $y=arctan\frac{1-x}{1+x}$.