How do you find the derivative of #(e^x)/(3+2x)#?

Answer 1

I would use the Quotient Rule:

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 find the derivative of (\frac{e^x}{3+2x}), you can use the quotient rule. The quotient rule states that for functions (f(x)) and (g(x)), the derivative of (\frac{f(x)}{g(x)}) is (\frac{f'(x)g(x) - f(x)g'(x)}{(g(x))^2}). Applying this rule:

Let (f(x) = e^x) and (g(x) = 3 + 2x).

(f'(x) = e^x) (derivative of (e^x) is itself) (g'(x) = 2) (derivative of (3 + 2x) is (2))

Now, plug these into the quotient rule:

[ \frac{d}{dx}\left(\frac{e^x}{3+2x}\right) = \frac{(e^x)(3 + 2x) - (e^x)(2)}{(3 + 2x)^2} ]

This simplifies to:

[ \frac{(e^x)(3 + 2x - 2)}{(3 + 2x)^2} ]

Further simplification yields the final derivative:

[ \frac{(e^x)(3 + 2x - 2)}{(3 + 2x)^2} = \frac{(e^x)(2x + 1)}{(3 + 2x)^2} ]

So, the derivative of (\frac{e^x}{3+2x}) is (\frac{(e^x)(2x + 1)}{(3 + 2x)^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