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Click the 'Go' button to instantly generate the derivative of the input function. The calculator provides detailed step-by-step solutions, facilitating a deeper understanding of the derivative process.
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The derivative of the sine inverse function is written as (sin-1 x)' = 1/√(1-x 2), that is, the derivative of sin inverse x is 1/√(1-x 2). In other words, the rate of change of sin -1 x at a particular angle is given by 1/√(1-x 2 ), where -1 < x < 1.
17 lis 2020 · To find the derivative of \(y = \arcsin x\), we will first rewrite this equation in terms of its inverse form. That is, \[ \sin y = x \label{inverseEqSine}\] Now this equation shows that \(y\) can be considered an acute angle in a right triangle with a sine ratio of \(\dfrac{x}{1}\).
The derivatives of inverse trigonometric functions can be computed by using implicit differentiation followed by substitution.
Derivative of the Inverse Sine Function. Use the inverse function theorem to find the derivative of g (x) = sin −1 x. g (x) = sin −1 x.
Free Derivative Calculator helps you solve first-order and higher-order derivatives. For trigonometric, logarithmic, exponential, polynomial expressions. Answers, graphs, alternate forms.
21 gru 2020 · Example \(\PageIndex{4}\): Derivative of the Inverse Sine Function. Use the inverse function theorem to find the derivative of \(g(x)=\sin ^{−1}x\). Solution. Since for \(x\) in the interval \([−\dfrac{π}{2},\dfrac{π}{2}],f(x)=\sin x\) is the inverse of \(g(x)=sin^{−1}x\), begin by finding \(f′(x)\). Since
