# Thread: [SOLVED] Extending Differentiation: Chain Rule

1. ## [SOLVED] Extending Differentiation: Chain Rule

Question:
Use the substitution $u = 5x + 3$ to differentiate the following with respect to $x$.

$(a) y = (5x + 3)^6$

$(b) y = (5x + 3)^{\frac{1}{2}}$

$(c) y = \frac{1}{5x + 3}$

Can you please show be the steps for solving $(a)$ using the chain rule?

2. Hello,

Substituting :

$y=u^6$

The chain rule says :

$y=f(u(x)) \Longleftrightarrow \frac{dy}{dx}=\frac{du}{dx} f'(u(x))$

Here, $f(u)=u^6$

$\frac{dy}{dx}=6 \frac{du}{dx} u^5$

$\frac{du}{dx}=5$

Hence $\frac{dy}{dx}=30u^5=30 (5x+3)^5$

Is it clear enough ?