Question

[SCREENSHOT INCLUDED] If y=2^(x^2+2), which of the following gives the slope of the tangent line for all values of x?

Answer 1

B)
`2xln(2)(2^(x^2+2))`

Explanation:

`y=2^(x^2+2)`

`y'=(d)/(dx)(2^(x^2+2))`

`y'=(d)/(dx)(e^((x^2+2)*ln(2)))`

`y'=(d)/(dx)(e^((x^2ln(2)+2ln(2))))`

`y'=2xln(2)*e^((x^2+2)(ln(2))`

`y'=2xln(2)(2^(x^2+2))`

Therefore,
`2xln(2)(2^(x^2+2))` is the slope of the tangent line