Quotient Rule At A Point

Finding a Critical Point of a Function

Procedure for Finding the Second Derivative

Solving for Where a Derivative Is Zero

Power Rule With Fractional Exponents

Product Rule With A Trigonometric Function

Average Rate of Change of a Function

Recalling Trigonometric Derivatives

Solve for x in the equation $$\frac{\sqrt{5*x+16}-\sqrt{5*x+9}}{x-2}=0.$$ Determine the solution set.

Evaluating a Derivative with Rational Exponents

Differentiability Implies Continuity

Differentiability of a Piecewise Function

Consider the function $$f(x)=\sqrt{\frac{x+3}{2*x-1}}.$$ Using the chain and quotient rules, its derivative simplifies to an expression which is never zero due to a nonzero constant factor in the numerator. Determine the solution to the equation $$f'(x)=0.$$

Exponential and Logarithmic Derivative Rules

Limit Definition of an Exponential Derivative

The limit $$\lim_{h\to0}\frac{(x+h)^3-x^3}{h}$$ represents the instantaneous rate of change of the function $$f(x)=x^3.$$ Setting this derivative equal to 12 gives the equation $$3x^2=12.$$ Solve for x.

Derivative of a Logarithmic Function

Piecewise Function Differentiability

Rank the following steps in the correct order for differentiating the composite function $$f(x)=(2*x+3)^5$$ using the Chain Rule together with the Power Rule.