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Calculus 1: Inverse and Hyperbolic Trig Derivatives

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

y=tan1(xy)y = \tan^{-1}(xy)

Show that ddx(arcsinx)=x1x2\frac{d}{dx}(\arcsin{x}) = \frac{x^{\prime}}{\sqrt{1 - x^2}}

Determine the derivative of the following inverse trig function

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

Determine the derivative of the inverse trigonometric function

f(x)=sec1(5x)f(x) = \sec^{-1}{(5x)}

Find the derivative of f(x)=2arccos(x3)f(x) = 2\arccos{(\frac{x}{3})}

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

Let f(x)=tan(x)f(x) = \tan{(x)} on the interval π2\frac{-\pi}{2} < xx < π2\frac{\pi}{2}

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

Show that for y=cos1(x)y = \cos^{-1}(x) the first derivative, dydx=1x2+1\frac{dy}{dx} = \frac{1}{x^2 + 1}

For the following function, find the first derivative

θ=tan1(2r)πr\theta = \frac{\tan^{-1}(2r)}{\pi{r}}

Find the derivative of the following hyperbolic function

f(x)=sin(sinh(x))f(x) = \sin{(\sinh{(x)})}

Find the derivative of f(x)=(sinh1(x))32f(x) = {(\sinh^{-1}(x))}^{\frac{3}{2}}

Find the derivative of sinh(x)\sinh{(x)} and cosh(x)\cosh{(x)}

Find the derivative of tanh(3x2+4x)\tanh{(3^{x^2} + 4x)}