# Use the instantaneous rate of change of #f(x) = e^(5x)# to find the equation of the tangent line to f(x) at x = 0?

##### 1 Answer

Jun 17, 2018

#### Answer:

#### Explanation:

The rate of change function of

This is also the gradient of the line tangent to the curve,

To determine

Thus the equation of the tangent line at

Sanity check the answer by plotting the two curves on the same graph and observing that they touch in the right place:

graph{(y-(e^(5x)))(y-(5x+1))=0 [-1, 1, -0.206, 2.291]}