# Product Rule

The Product Rule is a fundamental concept in calculus, specifically within the realm of differentiation. This rule provides a systematic approach to finding the derivative of the product of two functions. When dealing with functions that are products of two variables, the Product Rule offers a concise method for calculating how changes in one variable affect the overall function. In essence, it serves as a powerful tool in unraveling the complexities of mathematical functions, laying the groundwork for a deeper understanding of calculus and its applications.

Questions

- How do you differentiate #g(y) =xsqrtx # using the product rule?
- How do you differentiate #f(x)=e^(1+4x)*sin(5-x)# using the product rule?
- How do you find the derivative of #(3x+1)^(3/2) (2x+4)#?
- What is the derivative of #2x(4-x^2)^(1/2)#?
- What is the derivative of # y= xlnx#?
- How do you differentiate #y = x^2(sinx)^4 + x(cosx)^-2#?
- How do you differentiate #g(y) =(y^-1 + y^-2)(5y^2 -y^3)# using the product rule?
- How do you differentiate #f(x)= (4x^2-1) *ln x# using the product rule?
- How do you find the derivative of #f(x) = (x^3)(e^x)#?
- How do you differentiate #f(x)=x^3(4x - 12)# using the product rule?
- How do you differentiate #f(x)= (2x^2-5)(x+1) # using the product rule?
- How do you differentiate #f(x)=(sinx+1)(x^2-3e^x)# using the product rule?
- How do you differentiate #y=(x^5+1)(3x^2-x)#?
- How do you differentiate #g(y) =(4x^2+5)(x^2 - 1) # using the product rule?
- How do you differentiate #f(x)=sinxcosx# using the product rule?
- How do you differentiate #V(x)=(2x^3+3)(x^4-2x)#?
- How do you differentiate # f(x)= (4x^2+5)(3x-5)# using the product rule?
- How do you differentiate #y = x * sqrt (4 - x^2)#?
- How do you differentiate #f(x)=(4e^x+1)(x-3)# using the product rule?
- How do you find the derivative of #f(x)=(x^2) + (3 ln x)#?