Calculus
posted by Mel <3 .
Find the derivative of f(x) = x^2 ln (x^2) using the Product Rule, and simplify.

Let x^2 = u and ln(x^2) = 2 ln x = v
f'(x) = u dv/dx + v du/dx
f'(x) = x^2*(2/x) + 2x *2 ln x)
= 2x + 4 x ln x = 2 x (ln x + 1) 
y = (x^2) ln(x^2)
but ln(x^2) = 2 ln x
so
y = 2(x^2)ln x
dy/dx = 2(x^2) dy/dx (ln(x)) + 2 ln(x)dy/dx(x^2)
= 2 x^2 (1/x) + 2 ln x (2 x)
=2x +4x ln x
=2x(1+2lnx) 
My last equation was wrong. Damon is right
Respond to this Question
Similar Questions

Math, Calculus
Find the derivative of the function. y= xcosx  sinx What's the derivative? 
Calculus
How do I use the product rule to solve these two questions. Much appreciated! xo Find the derivative for k(x) = (5x4 + 2)(3sin x) Find the derivative for m(x) = ex cos x at x = 1 
Calculus
How do I use the chain rule to find the derivative of square root(1x^2) also, are there any general hints or tips for determining when the chain rule and product or quotient rule should be used? 
calculus
Find the derivative of y = (x^2 + 1)(x^3 + 1) in two ways: by using the Product Rule and by performing the multiplicatino first. Do your answers agree? 
Calculus
Find the derivative of y=x^2 / e^2x using the Quotient Rule, and simplify. I really need help! please! :) 
Further maths
Under differential calculus using the product rule find the derivative of (2x+3)^3(4x^21)^2 
calculus
Please help. Applying the chain rule, how do I find the derivative of f(x)=In(e^xe^x) (x>0) and then using this answer use the quotient rule to find the second derivative. I cannot do this so any answer greatly appreciated. 
Calculus (Derivatives)
Using the product rule, find the derivative of the following function: (x^1/2 cscx sinx). 
Calculus
What would an example of a logarithmic function that contains two trig functions within it where you would need to use chain rule and product rule to take derivative look like? 
Calculus
1.) Find the derivative of tan (sec x). 2.) Find the derivative if 1/x in four ways, using the limit process, power rule, quotient rule and implicit differentiation. 3.) Show that the derivative of sec^1 x is 1/(x*sqrt(x^2 1)). …