How do you differentiate #g(x) = sqrt(x-3)tanx# using the product rule?

Answer 1

#f=sqrt(x-3), g=tanx,f'=1/(2sqrt(x-3)) , g'=sec^2x#
#g'(x)=fg'+gf'=sqrt(x-3) sec^2x+tanx/(2sqrt(x-3)#

Sort the products into f and g, identify their derivatives, then enter all of that information into the product rule to make things simpler.

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

To differentiate ( g(x) = \sqrt{x-3} \tan(x) ) using the product rule, you can follow these steps:

  1. Identify the two functions being multiplied: ( f(x) = \sqrt{x-3} ) and ( h(x) = \tan(x) ).
  2. Apply the product rule: ( g'(x) = f'(x)h(x) + f(x)h'(x) ).
  3. Find the derivatives of each function:
    • ( f'(x) ) is the derivative of ( \sqrt{x-3} ).
    • ( h'(x) ) is the derivative of ( \tan(x) ).
  4. Substitute the derivatives and the original functions into the product rule formula.
  5. Simplify the expression to get the derivative ( g'(x) ).
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