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