Question

Please open the image and help me

Answer 1

1.

Looks like

`y=2\sqrt[3]{x}+\frac1{x^2}+\pi`

Write
`\sqrt[3]{x}` as a fractional power,
`x^(1/3)`. This makes it more obvious that the power rule should be used here.

`y'=(2x^(1/3))'+(x^(-2))'+\pi'`

`y'=\frac23x^(-2/3)-2x^(-3)`

`y'=\frac2{3\sqrt[3]{x^2}}-\frac2{x^3}`

2.

`y=(\sin(2x)+\tan(3x))^e`

Power and chain rule:

`y'=\left((\sin(2x)+\tan(3x))^e\right)'`

`y'=e(\sin(2x)+\tan(3x))^(e-1)(\sin(2x)+\tan(3x))'`

`y'=e(\sin(2x)+\tan(3x))^(e-1)(\cos(2x)(2x)'+\sec^2(3x)(3x)')`

`y'=e(\sin(2x)+\tan(3x))^(e-1)(2\cos(2x)+3\sec^2(3x))`