Calculus 1

What is the derivative of the following function

$f(x) = 15\sqrt[5]{x^2}$

Use the product rule to find the derivative of $y = 5x(x^2 - 2)$

Use the product rule to find the derivative of $y = (3x^2 + 2x) (2x^4 - 5)$

Find the first derivative of $y = 2x \sin({x^2})$

Find the derivative of $2^{3x} \cdot 5^{4x^2}$

Use the quotient rule to find the derivative of the following funciton,

$f(x) = \frac{x - 1}{x^2 + 2x + 1}$

Find $f\prime(x)$

$f(x) = \frac{5x^2 - 1}{2x^3 + 3}$

Given $f(x)$, find the equation of the tangent line at the point $(-1, -2)$

$f(x) = \frac{4x}{(1 + x^2)}$

Use the quotient rule to find the derivative of $y = \frac{5x}{6x^2 + 2x}$

Use the definition of the derivative to show that the derivative of $\sin{x}$ is equal to $\cos{x}$

Show that the derivative of $\cos{x}$ is equal to $-\sin{x}$

Show that the derivative of $\tan{x}$ is equal to $\sec^2{x}$

Use the quotient rule to find the derivative of $\sec{x}$

Use the quotient rule to find the derivative of $\csc{x}$

Find the derivative of the trig function, $f(x) = \sin{(x^2 + x)}$

What is the derivative of $y = x{}\cos{(x)}$

Find the derivative of $y = \frac{\tan{(2x)}}{x^2}$

Use the definition of $e$ as the unique positive number for which $\lim_{h\rightarrow 0}\frac{e^{h} - 1}{h} = 1$ and the definition of the derivative to show that derivative of the exponential function, $f(x) = e^x$ is equal to $e^x$

Determine the derivative of $f(x) = 2x^5 - 3e^{6x}$

Find the derivative of $f(x) = x^{3}e^{-2x}$