Question

find the derivative of f(x).
f(x)=(7x - 4)^4
f(x)=

Explanation:

Step1: Let \( u = 7x - 4 \)

Then \( f(x)=u^{4} \).

Step2: Find derivatives of \( u \) and \( f(u) \)

The derivative of \( u \) with respect to \( x \): \( \frac{du}{dx}=7 \).
The derivative of \( f(u)=u^{4} \) with respect to \( u \): \( \frac{df}{du} = 4u^{3} \).

Step3: Apply the chain rule \( \frac{df}{dx}=\frac{df}{du}\cdot\frac{du}{dx} \)

Substitute \( u = 7x - 4 \), \( \frac{df}{du}=4u^{3} \), and \( \frac{du}{dx}=7 \) into the chain - rule formula.
\( \frac{df}{dx}=4(7x - 4)^{3}\cdot7 \).

Step4: Simplify the expression

\( \frac{df}{dx}=28(7x - 4)^{3} \).

Answer:

\(28(7x - 4)^{3}\)