Home > Calculus > Derivatives of y=sec(x), y=cot(x), y= csc(x)

How do you find the derivative of #y=tan^2(5x)#?

Answer 1

Emma Aldridge

#dy/dx=10tan5xsec^2 5x#

#"differentiate using the "color(blue)"chain rule"#

#"Given "y=f(g(x))" then"#

#dy/dx=f'(g(x))xxg'(x)#

#y=tan^2 5x=(tan5x)^2#

#rArrdy/dx=2tan5x xxd/dx(tan5x)#

#color(white)(rArrdy/dx)=2tan5x xxsec^2 5x xxd/dx(5x)#

#color(white)(rArrdy/dx)=10tan5xsec^2 5x#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

William Abdalla

To find the derivative of ( y = \tan^2(5x) ), you can use the chain rule. First, find the derivative of ( \tan^2(u) ), where ( u = 5x ), then multiply by the derivative of ( u = 5x ). The derivative is ( \frac{dy}{dx} = 10 \tan(5x) \sec^2(5x) ).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.