Advertisements
Advertisements
प्रश्न
find dy/dx if `y=tan^-1((6x)/(1-5x^2))`
Advertisements
उत्तर
Let ` y=tan^-1((6x)/(1-5x^2))`
`=tan^-1((x+5x)/(1-5x^2))`
`y=tan^-1(x)+tan^-1(5x)`
Differentiating w.r.t x
`dy/dx=1/(1+x^2)+1/(1+25x^2)xx5`
`=1/(1+x^2)+5/(1+25x^2)`
APPEARS IN
संबंधित प्रश्न
Find `dy/dx if y=cos^-1(sqrt(x))`
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`
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?
What condition is required for \[\frac{\mathrm{d}x}{\mathrm{d}y}=\frac{1}{\left(\frac{\mathrm{d}y}{\mathrm{d}x}\right)}\]?
Which derivative and condition are correct for \[\sin^{-1}x\]?
Which derivative and condition are correct for \[\cos^{-1}x\]?
Which expression is the derivative of \[\cos^{-1}(f(x))\] when \[|f(x)|<1\]?
Which derivative and condition are correct for \[\cot^{-1}x\]?
Which derivative and condition are correct for \[\operatorname{cosec}^{-1}x\]?
Which expression is the derivative of \[\operatorname{cosec}^{-1}(f(x))\] when \[|f(x)|>1\]?
Let \[y=\sin^{-1}x\]. What inverse relation is used for implicit differentiation?
Which inverse functions have denominator \[1+x^2\] in their derivatives?
For which inverse functions are negative signs especially important?
What must be checked before applying derivative formulas for inverse functions?
