What is the derivative of #y=sec(3x^2)#?

Answer 1

By the chain rule:

Let #y = sec(u)# and #u = 3x^2#.
The derivative of #secx# can be found by the following proof:
#secx = 1/cosx#
#(1/cosx)' = ((0 xx cosx) - (1 xx -sinx))/(cosx)^2#
#(1/cosx)' = sinx/(cos^2x)#
#(secx)' = secx xx sinx/cosx#
#(secx)' = secxtanx#
The derivative of #3x^2# can be obtained using the power rule:
#(3x^2)' = 2 xx 3x^(2 - 1)#
#(3x^2)' = 6x#
The chain rule states that #dy/dx = dy/(du) xx (du)/dx#.
Hence, #dy/dx = secutanu xx 6x = 6xsec(3x^2)tan(3x^2)#

Practice exercises:

a) #cscx#
b) #cot(3x^2 + 5x + 1)#
c) #tan(e^(2x^2))#

Hopefully this helps, and good luck!

Sign up to view the whole answer

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

Sign up with email
Answer 2

The derivative of ( y = \sec(3x^2) ) is ( y' = 6x \sec(3x^2) \tan(3x^2) ).

Sign up to view the whole answer

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

Sign up with email
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.

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.

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.

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.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7