Calculus
# Differentiation Rules

$f(x) = e^x \cdot \sin x$

For non-zero values of $f(x)$, simplify the expression below. $\log_{2} \dfrac{f^{(2016)} (x)}{f(x)}$

**Notation**: $f^{(n)}(x)$ denotes the $n^\text{th}$ derivative of $f(x)$.

$\large { \left. \frac { d }{ d(\cos { (x) } ) } \cos { (2015x) } \right\vert _{ x=2\pi } } = \ ?$

Find a closed-form expression for the following derivative.

$\frac{d}{d(x^{n})}x^{y}$

${F(x)} = {f(x)g(x)h(x)}$

The above equation is true for all real $x$, where $f(x)$, $g(x)$ and $h(x)$ are differentiable functions at some point $a$.

Given $F '(a) = 21 F(a), f '(a) = 4f(a), g'(a) = -7g(a), h'(a) = kh(a)$. Find $k$.