Find the derivative of h(x) = {4}^{ (x)/(2) } \sin(2x)

Question

Find the derivative of
`h(x) = {4}^{ (x)/(2) } \sin(2x)`

Answer 1

The given expression is:

`\begin{gathered} \\ h(x)={4}^{(x)/(2)}\sin (2x) \end{gathered}`

To find the derivative, use the product rule:

`\begin{gathered} (dh)/(dx)=\text{ U}(dV)/(dx)+V(dU)/(dx) \\ U=4^{(x)/(2)} \\ (dU)/(dx)=\text{ }\frac{4^{(x)/(2)}\ln 4}{2} \\ V\text{ = sin(2x)} \\ (dV)/(dx)=\text{ 2}\cos (2x) \end{gathered}`

Substitute, U, V, dU/dx, and dV/dx into the product rule given above: