Derivative of Secant: Find dy/dx

[Karol]

Homework Statement

Find dy/dx for $~y=\sec^2(5x)$

Homework Equations

Secant and it's derivative:
$$\sec\,x=\frac{1}{\cos\,x}$$
$$\sec'\,x=\tan\,x\cdot\sec\,x$$

The Attempt at a Solution

$$y=\sec^2(5x)~\rightarrow~y'=2\cdot 5 \cdot \sec(5x)\tan(5x)\sec(5x)=10\tan(5x)\sec^2(5x)$$
The answer should be:
$$y'=-\frac{2x+1}{2}\frac{1}{\sqrt{(x^2+x-1)^3}}$$

 

[jambaugh]

Your solution is correct to the given problem.

 

[Karol]

Thank you very much jambaugh