Question

Find dy/dx, if y= 5e^x/cosx

Answer 1

y = (5e^x)/(cos x)
Since 1/cos(x) = sec(x), we can also rewrite this as
(5e^x)(sec(x))
Since two terms which are both functions of x are multiplied, we use the chain rule. Thus it becomes:
(5e^x)(sec(x)) + (5e^x)(tan(x) * sec(x))
Simplifying,
dy/dx = (5e^x)(sec(x))(1 + tan(x))

Hope this helps~ :3

Answer 2

Let f(x) = e^x
So f'(x) = e^x
Let g(x) = cos(x)
So g'(x) = -sin(x)

Use:
(f/g)' = ((f'×g)-(f×g'))/g^2