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

Answer:

B) $2xln(2)(2^{x^2+2})$

Step-by-step explanation:

$y=2^{x^2+2}$

$y'=\frac{d}{dx}(2^{x^2+2})$

$y'=\frac{d}{dx}(e^{(x^2+2)*ln(2)})$

$y'=\frac{d}{dx}(e^{(x^2ln(2)+2ln(2))})$

$y'=2xln(2)*e^{(x^2+2)(ln(2)}$

$y'=2xln(2)(2^{x^2+2})$

Therefore, $2xln(2)(2^{x^2+2})$ is the slope of the tangent line