Question

find the derivative of the function w, below. it may be to your advantage to simplify first.
w = \frac{y^{8}-3y^{3}+14y}{y}
\frac{dw}{dy}=

Explanation:

Step1: Simplify the function

Divide each term in the numerator by $y$: $w=\frac{y^{8}}{y}-\frac{3y^{3}}{y}+\frac{14y}{y}=y^{7}-3y^{2} + 14$.

Step2: Apply power - rule for derivatives

The power - rule states that if $f(x)=x^{n}$, then $f^\prime(x)=nx^{n - 1}$. For $w = y^{7}-3y^{2}+14$, the derivative of $y^{7}$ is $7y^{6}$, the derivative of $-3y^{2}$ is $-3\times2y=-6y$, and the derivative of the constant 14 is 0.
So, $\frac{dw}{dy}=7y^{6}-6y$.

Answer:

$7y^{6}-6y$