# Power Rule

The Power Rule in calculus is a fundamental principle used to differentiate functions of the form \( f(x) = x^n \), where \( n \) is any real number. This rule states that the derivative of \( f(x) \) with respect to \( x \) is \( f'(x) = nx^{n-1} \). In simpler terms, it allows us to find the slope of the tangent line to the graph of \( f(x) \) at any point \( x \). The Power Rule is particularly useful in many areas of science, engineering, and economics where rates of change are important, making it a foundational concept in calculus.

Questions

- How do you find the derivative of #y =sqrt(x-1)#?
- How do you find the derivative of #y=5+sinx#?
- If #F(x) = x^(2/3)# What is #f'(x)# ?
- How do you differentiate #f(x)=x+1+(x+2)^2#?
- How do you find the derivative of #f(x)=sqrt(ax+b)#?
- How do you differentiate #V=4/3pi^3+8pir^2#?
- How do you find the derivative of #5xe^(2x)#?
- How do you find the derivative of # f(x)=x^3-x#?
- How do you find the derivative of #y=pi/2sintheta-costheta#?
- What is the derivative of #-x#?
- What is the antiderivative of a constant?
- How do you differentiate #x^sqrt5+sqrt(5x)#?
- How do you differentiate #x+4/x#?
- How do you find the derivative of #x^2+1#?
- How do you find the derivative of #g(x)=xsqrtx#?
- How do you find the derivative of #f(x)=(x+1)(x^2+2x-3)#?
- How do you differentiate #F(x)=3/4x^8#?
- How do you find the derivative of #x^(1/3)#?
- What is the derivative of #32/x#?
- What is the #n^(th)# derivative of #x^(-1/2) #?