Question

find the slope of the tangent to the function F(x)=2^(x^2+3x) when x=3

Answer 1

You need to evaluate the derivative at 3

Answer 2

The slope of the tangent is simply the value of the first derivative. So to find the slope of the tangent at x=3, we first find the derivative and then we plug it in 3 for x.

The first derivative of c^u (where u is a function of x) is

(c^u)(u')(ln(c)), where u' is the first derivative of u and ln(c) is the natural log.

So for 2^(x^2+3x), the first derivative is

[2^(x^2+3x)][2x+3][ln(2)]

We can then plug in 3 for x

[2^(3^2+3(3))][2(3)+3][ln(2)]

Then, simplify to get your answer