Answer:
[tex]\frac{dy}{dx}=4\sin (4x-3)[/tex]
Explanation:
Given the following functions:
[tex]\begin{gathered} y=\cos u \\ u=4x-3 \end{gathered}[/tex]
We find the derivative below:
[tex]\begin{gathered} \frac{dy}{dx}=f^{\prime}\lbrack g(x)\rbrack g^{\prime}(x) \\ Since\text{ u=g(x)} \\ \frac{dy}{dx}=f^{\prime}\lbrack u\rbrack u^{\prime} \end{gathered}[/tex]
Since y=f(u)
[tex]\begin{gathered} \frac{dy}{dx}=\frac{dy}{du}\times\frac{du}{dx} \\ =\sin u\times4 \\ =4\sin u \end{gathered}[/tex]
Substitute u=4x-3 into dy/dx:
[tex]\frac{dy}{dx}=4\sin (4x-3)[/tex]
