# How do I find the derivative of #F(y) = yln(9 + e^y)#?

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

To find the derivative of F(y) = yln(9 + e^y), you can use the product rule and the chain rule of differentiation.

- Apply the product rule: (uv)' = u'v + uv'
- Let u = y and v = ln(9 + e^y)
- Find the derivatives of u and v.
- u' = 1
- v' = (1/(9 + e^y)) * (e^y)

- Substitute u', v', u, and v into the product rule formula.
- F'(y) = (1)(ln(9 + e^y)) + (y)((1/(9 + e^y)) * (e^y))

- Simplify the expression.
- F'(y) = ln(9 + e^y) + (y * e^y) / (9 + e^y)

So, the derivative of F(y) = yln(9 + e^y) is F'(y) = ln(9 + e^y) + (y * e^y) / (9 + e^y).

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

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.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7