Question

Y = (4x ^ 2 + 7e ^ x) ^ (1/3); Find * (dy)/(dx)

Answer 1

Given

`y=(4x^2+7e^x)^{(1)/(3)}`

To find dy/dx.

Step-by-step explanation:

It is given that,

`y=(4x^2+7e^x)^{(1)/(3)}`

That implies,

`\begin{gathered} (dy)/(dx)=(d)/(dx)(\left(4x^2+7e^x\right)^{(1)/(3)}) \\ =(1)/(3)\left(4x^2+7e^x\right)^{(1)/(3)-1}*(4*2x+7e^x) \\ =(1)/(3)\left(4x^2+7e^x\right)^{(1-3)/(3)}*(8x+7e^x) \\ =(1)/(3)\left(4x^2+7e^x\right)^{-(2)/(3)}*(8x+7e^x) \\ =\frac{8+7e^x}{3\left(4x^2+7e^x\right)^{(2)/(3)}} \end{gathered}`

Hence, the derivative is,

`(dy)/(dx)=\frac{8x+7e^x}{3\left(4x^2+7e^x\right)^{(2)/(3)}}`