Find the derivative of $$y = e^{\sin(2*x)}$$ with respect to x.

Differentiability of a Piecewise Function

I. Differentiating $$\cos(x)+\cos(y)=1$$ implicitly results in $$-\sin(x)-\sin(y)*(dy/dx)=0$$. II. Solving yields $$dy/dx=-\frac{\sin(x)}{\sin(y)}$$. III. At a point where $$\sin(y)=0$$, the tangent line to the curve is horizontal. Which of the above statements is/are true?

Derivative of a Product at a Point

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 $$f'(x)=0.$$

Power Rule for Differentiation

Limit Definition of the Derivative

Given the function $$f(x)= 3*x^2+2$$, find the average rate of change of $$f(x)$$ from $$x=1$$ to $$x=4$$.

Limit Definition of the Derivative

Derivative of a Polynomial Function

Differentiability of a Piecewise Function

Using the graph of $$f(x)=\sin(x)$$, find the derivative $$f'(x)$$ using the limit definition of the derivative.

Average Rate of Change on an Interval

From the graph above, if the tangent line to f(x) at $$x=2$$ has a slope of $$5$$ and passes through the point $$(2, 3)$$, what is its equation?

Tangent Line to a Cosine Function

Marginal Profit and Production Level

Differentiability of a Piecewise Function

Determine the derivative of $$f(x)=\ln(x^2+1)$$ using the chain rule as suggested by the graph.

Evaluating a Derivative at a Point

Properties of the Difference Quotient