Derivatives of Inverse Trig Functions
Read this topicExplanations 4
- Suppose we want to find the derivative of f−1(x)f^{-1}(x)f−1(x) for some function f(x)f(x)f(x). Well, from Derivative of Inverse, we know ddxf−1(x)=1f′(f−1(x))\frac{\text d}{\te…
By Jack Gurev, Tim Ratigan, Victor Wang, Andrew Machkasov, Yang Liu, Moor Xu
- Here is some practice with taking derivatives of inverse functions, good luck!
By Freya Edholm
- (Videos) Derivatives of Inverse Trig Functions by PatrickJMT Here's a video by patrickJMT showing you how to take the derivative of inverse trigonometric functions. Inverse trig…
By Alex Federspiel
- (Video) Deriving the Derivative of Inverse Tangent by PatrickJMT Here's a good video by patrickJMT showing you how to derive the derivative of inverse tangent. This is helpful b…
By Alex Federspiel
Problems 11
- Let y=xxy = x^xy=xx for x>0x > 0x>0. What is dydx\frac{dy}{dx}dxdy?
- What is the derivative of xxx with respect to y=sinxy = \sin xy=sinx?
- Find the derivative. y=(1+x)2arctanxy=(1+x)^2\arctan xy=(1+x)2arctanx
- Find the derivative. f(x)=e−csc−1xf(x)=e^{-\csc^{-1}x}f(x)=e−csc−1x
- Find the derivative. g(t)=cot−1(2t)+cot−1(2t)g(t)=\cot^{-1}(2t)+\cot^{-1}\bigg(\frac2t\bigg)g(t)=cot−1(2t)+cot−1(t2)
- Find the derivative. arctan(xy)=1+xy\arctan(xy)=1+xyarctan(xy)=1+xy
- Find the derivative. f(x)=arcsinesinxf(x)=\arcsin{e^{\sin x}}f(x)=arcsinesinx
- Find the derivative. λ(t)=ln(sin−1tcos−1t)\lambda(t)=\ln\bigg(\frac{\sin^{-1}t}{\cos^{-1}t}\bigg)λ(t)=ln(cos−1tsin−1t)
- Find the derivative. y=2csc−1xsec−1xy=2^{\csc^{-1}x}\sec^{-1}xy=2csc−1xsec−1x
- Find the derivative. y=arcsin(2x−x4)y=\arcsin(\sqrt{2x-x^4})y=arcsin(2x−x4)
- Find the second derivative. y=arcsin(ex)y=\arcsin(e^x)y=arcsin(ex)