Ali tried to find the derivative of $(5 x-6)^{7}$. Here is his work:

Step 1: This is a composite function. The inner function is ${u}({x})=5 {x}-6$ and the outer function is ${w}({x})=x^{7}$

Step 2: We should use the chain rule:

$\frac{d}{d x}[w(u(x))]=w^{\prime}(u(x)) \cdot u^{\prime}(x)$

Step 3: Finding the derivatives of the inner and outer functions:

$w^{\prime}(x)=7 x^{6} \text { and } u^{\prime}(x)=5$

Step 4: Putting it all together:

$\frac{d}{d x}[(5 x-6)^{7}]=7(5 x-6)^{6} \cdot(5)$

$=35(5 x-6)^{6}$

Is Ali’s work correct? If not, what’s his mistake?