# Chain Rule

The chain rule is a fundamental concept in calculus that enables the differentiation of composite functions. It provides a method for finding the derivative of a function that is composed of two or more functions by breaking it down into simpler parts. By understanding how changes in one function affect changes in another, the chain rule allows mathematicians to efficiently calculate derivatives in complex scenarios. Essential for various applications in mathematics, physics, engineering, and more, the chain rule serves as a cornerstone in understanding the dynamics of interconnected systems and relationships between variables.

Questions

- How do you differentiate #f(x)=cot(sqrt(x^2-1)) # using the chain rule?
- What is the derivative of #cos^7(e^x)#?
- How do you find the derivative of #f(x)=(5x^6sqrt x) + (3/(x^3 sqrt x))#?
- How do you find the derivative of #x^lnx#?
- What is the derivative of #cos(pi x)#?
- How do you find the derivative of #y=(4x+3)^-1+(x-4)^-2#?
- How do you use the chain rule to differentiate #y=(cosx/(1+sinx))^5#?
- How do you use the chain rule to differentiate #y=7/(2x+7)^2#?
- What is the derivative of #xsqrt(1-x)#?
- How do you use the chain rule to differentiate #y=root5(x^2-3)/(-x-5)#?
- How do you differentiate #f(t)=sin^2(e^(sin^2t))# using the chain rule?
- What is the second derivative of # (x^2-1)^3#?
- How do you find the derivative of #cos^2(x^2-2)#?
- How do you differentiate # f(x)= (6e^(-x)+2)^3 # using the chain rule?
- How do you differentiate #f(x) = ln(sqrt(arcsin(e^(2-x^2)) ) # using the chain rule?
- How do you find the derivative of #x*sqrt(x+1)#?
- How do you find the derivative of #3*(sqrtx) - (sqrtx^3)#?
- How do you differentiate #f(x)=(x^2-2x)^2# using the chain rule?
- How do you differentiate #f(x)=sece^(4x)# using the chain rule.?
- How do you differentiate #f(x)= ln(2x+1)^(-1/2) #?