Question

Find the derivative of: 3x^5+5x^9

Answer 1

`\frac{\text{d}y}{\text{d}x} =15x^4+45x^8`

Explanation:

`\boxed{\begin{minipage}{4.8 cm}\underline{Differentiating $ax^n$}\\\\If $y=ax^n$, then $\frac{\text{d}y}{\text{d}x}=nax^(n-1)$\\\end{minipage}}`

`\textsf{Differentiate $y$ with respect to $x$}:`

`\begin{aligned}y & = 3x^5+5x^9\\\\\implies \frac{\text{d}y}{\text{d}x} & = 5 \cdot 3x^(5-1)+9 \cdot 5x^(9-1)\\\\& = 15x^4+45x^8\end{aligned}`

`\textsf{Therefore, the derivative of $y$ with respect to $x$ is: $\frac{\textrm{d}y}{\textrm{d}x} =15x^4+45x^8$}`