Calculus 1

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 $f(x) = x^{3}e^{-2x}$

Determine the slope of the tangent line to the function $f(x) = 2e^{-3x}$at $(0,2)$

For the following problem, find the derivative of $f(x) = 5^{x^{3} - 4}$

Use logarithmic differentiation to find the derivative in the following example

$g(x) = \log_{3}(2x^{2} - 5x)$

Find the derivative of $h(x) = 8^{x}\log_{9}x$

Use the properties of logarithms to show that the derivative of $\log_{a}x = \frac{1}{(\ln{a})x}$

Use implicit differentiation to show that the derivative of $\ln{x} = \frac{1}{x}$ for $x > 0$

Note that many classes introduce logarithmic differentiation before implicit differentiation.

Differentiate $f(x) = \ln{6x^2}$

Find the derivative of $f(x) = \frac{\ln{(2x)}}{x^4}$

Use the chain rule to find the derivative of the following function,

$f(x) = {(4x^2 + 5)}^{10}$

Use the chain rule to find the derivative of the following function

$f(x) = \sqrt{3x^3 + 10x}$

Find the derivative of $f(x) = \frac{2}{5x^2 + 3x}$

Given $y = 4 (3x + 4)^5$ find $\frac{dy}{dx}$

Find the derivative of $y = {(2x - 5)}^2$

Practice the chain rule by finding the derivative of the following function

$y = \sqrt{3x + 4}$

Find the derivative of $y = \sin{(3x^2 - 1)}$

Find the derivative of $y = {(x^2 + 3x)}^7$

Find the derivative of the following function

$y = \frac{\ln{(x - 1)}}{\sqrt{x^{\pi} + 1}}$