# What is the derivative of # y= xlnx#?

# dy/dx = 1 + lnx #

We have:

Using the product rule, we can obtain:

Observing a typical calculus outcome:

We get:

Corollary As we've just demonstrated,

Now that we have integrated both sides, we obtain:

Hence:

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

To find the derivative of ( y = x \ln(x) ), you can use the product rule of differentiation, which states that the derivative of the product of two functions is the derivative of the first function times the second function, plus the first function times the derivative of the second function.

So, applying the product rule to ( y = x \ln(x) ), we have:

[ y' = \frac{d}{dx} (x) \cdot \ln(x) + x \cdot \frac{d}{dx} (\ln(x)) ]

[ y' = 1 \cdot \ln(x) + x \cdot \frac{1}{x} ]

[ y' = \ln(x) + 1 ]

Therefore, the derivative of ( y = x \ln(x) ) is ( \ln(x) + 1 ).

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.

- How do you differentiate #f(x)=cos(e^(3x^2)+7) # using the chain rule?
- How do you differentiate #(sin^2x+sin^2y)/(x-y)=16#?
- How do you differentiate #g(y) =(x^2 - 1) (x^2 - 2x + 1)^4 # using the product rule?
- How do you use the chain rule to differentiate #f(x)=cos(2x^2+3x-sinx)#?
- How do you differentiate # f(x)=ln(1/sqrt(e^x-x))# using the chain rule.?

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