Calculus 1

Find the derivative of the following function

$f(n) = \sin{(n^2 + e^n + 1)}$

Use implicit differentiation to find $\frac{dy}{dx}$ for the following equation

$x^2 + y^2 = 25 + 5x$

For the following function, find $\frac{dy}{dx}$ by implicit differentiation

$x^2 + 2xy + y^2 = 5$

Use implicit differentiation to take the derivative of $y$ with respect to $x$ for the following equation

$y^5 + 2y = x^2$

Find $\frac{dy}{dx}$ when $x^3 + 3y^4 = 2x + 7$

Find the derivative of $y$ with respect to $x$ for the following equation

$y(x+4) = x^2 - 3$

Find $\frac{dy}{dx}$ for $x^2 + y^3 = \log{(x + y)}$

Find the derivative, $y^{\prime}$ of the following implicit function

$y = \tan^{-1}(xy)$

For the following equation, differentiate implicitly to find $\frac{dy}{dx}$

$e^{(x + y)} = \sin{(x)} + \cos{(y)}$

Find the tangent line to the curve $xy + \ln{(xy^2)} = 1$ at the point $(1,1)$

Find $\frac{dy}{dx}$ and the slope of the tangent line at $(-2, 1)$ for the curve given by

$2x^2 - 3y^3 = 5$

Find $\frac{dy}{dx}$ and the slope of the tangent line at (0,3) for the curve given by

$y^3 + x^{2}y^{5} - x^4 = 27$

Determine the first and second derivatives, $\frac{dy}{dx}$ and $\frac{d^{2}y}{dx^2}$ for the following equation

$x^2 + xy = 4$

Show that $\frac{d}{dx}(\arcsin{x}) = \frac{x^{\prime}}{\sqrt{1 - x^2}}$

Determine the derivative of the following inverse trig function

$f(x) = \arctan{(\sqrt{x})}$

Determine the derivative of the inverse trigonometric function

$f(x) = \sec^{-1}{(5x)}$

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

Determine the derivative of $f(t) = \sin{(\arccos{(t)})}$

Let $f(x) = \tan{(x)}$ on the interval $\frac{-\pi}{2}$ < $x$ < $\frac{\pi}{2}$

What is $\frac{d}{dx}(\arctan{(x)})$ ?

Show that for $y = \cos^{-1}(x)$ the first derivative, $\frac{dy}{dx} = \frac{1}{x^2 + 1}$