Advertisements
Advertisements
प्रश्न
If `y=cos^-1(2xsqrt(1-x^2))`, find dy/dx
Advertisements
उत्तर
`y=cos^-1(2xsqrt(1-x^2))`
put `x=sintheta`
`theta =sin^-1x`
`=cos^-1(2sinthetasqrt(1-sin^2theta))`
`=cos^-1(sin2theta)`
`=cos^-1(cos(pi/2-2theta))`
`y=pi/2-2theta=pi/2-2sin^-1x`
Differentiating with respect to 'x', we get
`dy/dx=0 -2/sqrt(1-x^2) = (-2)/sqrt(1-x^2)`
APPEARS IN
संबंधित प्रश्न
find dy/dx if `y=tan^-1((6x)/(1-5x^2))`
If `y=sec^-1((sqrtx-1)/(x+sqrtx))+sin_1((x+sqrtx)/(sqrtx-1)), `
(A) x
(B) 1/x
(C) 1
(D) 0
If y = f(x) is a differentiable function of x such that inverse function x = f–1 (y) exists, then prove that x is a differentiable function of y and `dx/dy=1/((dy/dx)) " where " dy/dx≠0`
If y = f (x) is a differentiable function of x such that inverse function x = f –1(y) exists, then
prove that x is a differentiable function of y and
`dx/dy=1/(dy/dx)`, Where `dy/dxne0`
Hence if `y=sin^-1x, -1<=x<=1 , -pi/2<=y<=pi/2`
then show that `dy/dx=1/sqrt(1-x^2)`, where `|x|<1`
Find `dy/dx` if `y = tan^(-1) ((5x+ 1)/(3-x-6x^2))`
If `x^y = e^(x - y)` , show that `(dy)/(dx) = logx/(1 + logx)^2`
The total cost function of a firm is C = x2 + 75x + 1600 for output x. Find the output for which the average cost ls minimum. Is CA= Cm at this output?
If \[y=f(x)\] is a differentiable function of \[x\] and the inverse function \[x=f^{-1}(y)\] exists, which expression gives \[\frac{\mathrm{d}x}{\mathrm{d}y}\]?
What condition is required for \[\frac{\mathrm{d}x}{\mathrm{d}y}=\frac{1}{\left(\frac{\mathrm{d}y}{\mathrm{d}x}\right)}\]?
The derivative of an inverse function is usually found using which method?
Which derivative and condition are correct for \[\sin^{-1}x\]?
Which expression is the derivative of \[\sin^{-1}(f(x))\] when \[|f(x)|<1\]?
Which derivative and condition are correct for \[\cos^{-1}x\]?
Which expression is the derivative of \[\tan^{-1}(f(x))\] when \[f(x)\in\mathbb{R}\]?
Which expression is the derivative of \[\cot^{-1}(f(x))\] when \[f(x)\in\mathbb{R}\]?
Which derivative and condition are correct for \[\sec^{-1}x\]?
Which expression is the derivative of \[\sec^{-1}(f(x))\] when \[|f(x)|>1\]?
Which derivative and condition are correct for \[\operatorname{cosec}^{-1}x\]?
Let \[y=\sin^{-1}x\]. What inverse relation is used for implicit differentiation?
Differentiating \[x=\sin y\] with respect to \[x\] gives which equation?
Using \[\sin^2y+\cos^2y=1\] and \[\sin y=x\], what is \[\cos^2y\]?
For \[y\in\left(-\frac{\pi}{2},\frac{\pi}{2}\right)\], which value of \[\cos y\] follows from \[\cos^2y=1-x^2\]?
Which inverse functions have denominator \[1+x^2\] in their derivatives?
Which inverse functions have a denominator involving \[|x|\sqrt{x^2-1}\]?
For which inverse functions are negative signs especially important?
What must be checked before applying derivative formulas for inverse functions?
