Question

What is the slope of the curve y= 2^(x^(2)+1) at x=1? answers 1)8/ln2 2)8 3)8ln2 4)10ln2

Answer 1

Find the derivative of the function, but you have to rewrite it:

\[y = 2^{x^2+1}=e ^{\ln 2^{x^2+1}}=e ^{(x^2+1)\ln 2}\]

Use the chain rule on the last one to get:

\[y' = e ^{(x^2+1)\ln 2}*2x \ln 2 = 2\ln2*x*2^{x^2+1}\]

Let x = 1 to find the slope of the curve at x = 1.

y'(1) = 2ln2*1*2^2= 2*4ln 2 = 8ln 2