Answer:
[tex]\dfrac{\text{d}y}{\text{d}x} =15x^4+45x^8[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4.8 cm}\underline{Differentiating $ax^n$}\\\\If $y=ax^n$, then $\dfrac{\text{d}y}{\text{d}x}=nax^{n-1}$\\\end{minipage}}[/tex]
[tex]\textsf{Differentiate $y$ with respect to $x$}:[/tex]
[tex]\begin{aligned}y & = 3x^5+5x^9\\\\\implies \dfrac{\text{d}y}{\text{d}x} & = 5 \cdot 3x^{5-1}+9 \cdot 5x^{9-1}\\\\& = 15x^4+45x^8\end{aligned}[/tex]
[tex]\textsf{Therefore, the derivative of $y$ with respect to $x$ is: $\dfrac{\textrm{d}y}{\textrm{d}x} =15x^4+45x^8$}[/tex]
