# How do you find the derivative of #y=xlnx#?

Use the product rule.

You'll need the product rule for this one. The product rule is given by:

Hope this helps!

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, which states that if ( u(x) ) and ( v(x) ) are differentiable functions of ( x ), then the derivative of their product is ( (u v)' = u'v + uv' ).

Let ( u(x) = x ) and ( v(x) = \ln x ).

Then, ( u'(x) = 1 ) (since the derivative of ( x ) with respect to ( x ) is 1) and ( v'(x) = \frac{1}{x} ) (the derivative of ( \ln x ) with respect to ( x ) is ( \frac{1}{x} )).

Now, applying the product rule:

[ \frac{d}{dx}(x \ln x) = u'v + uv' ] [ = (1)(\ln x) + (x)\left(\frac{1}{x}\right) ] [ = \ln x + 1 ]

So, 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.

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