Advertisements
Advertisements
प्रश्न
If \[3 \sin \left( xy \right) + 4 \cos \left( xy \right) = 5, \text { then } \frac{dy}{dx} =\] _____________ .
पर्याय
\[- \frac{y}{x}\]
\[\frac{3 \sin \left( xy \right) + 4 \cos \left( xy \right)}{3 \cos \left( xy \right) - 4 \sin \left( xy \right)}\]
\[\frac{3 \cos \left( xy \right) + 4 \sin \left( xy \right)}{4 \cos \left( xy \right) - 3 \sin \left( xy \right)}\]
none of these
उत्तर
\[- \frac{y}{x}\]
\[\text { We have, } 3 \sin\left( xy \right) + 4 \cos\left( xy \right) = 5 \]
\[ \Rightarrow 3 \cos\left( xy \right)\left[ x\frac{dy}{dx} + y \right] - 4 \sin\left( xy \right)\left[ x\frac{dy}{dx} + y \right] = 0\]
\[ \Rightarrow \left[ x\frac{dy}{dx} + y \right]\left[ 3 \cos\left( xy \right) - 4 \sin\left( xy \right) \right] = 0\]
\[ \Rightarrow x\frac{dy}{dx} + y = 0\]
\[ \Rightarrow x\frac{dy}{dx} = - y\]
\[ \therefore \frac{dy}{dx} = - \frac{y}{x}\]
APPEARS IN
संबंधित प्रश्न
Differentiate the following functions from first principles ecos x.
Differentiate sin (3x + 5) ?
Differentiate \[3^{x^2 + 2x}\] ?
Differentiate \[\sin \left( 2 \sin^{- 1} x \right)\] ?
Differentiate \[3 e^{- 3x} \log \left( 1 + x \right)\] ?
If \[y = \frac{1}{2} \log \left( \frac{1 - \cos 2x }{1 + \cos 2x} \right)\] , prove that \[\frac{ dy }{ dx } = 2 \text{cosec }2x \] ?
Differentiate \[\tan^{- 1} \left( \frac{a + b \tan x}{b - a \tan x} \right)\] ?
If \[y = \cot^{- 1} \left\{ \frac{\sqrt{1 + \sin x} + \sqrt{1 - \sin x}}{\sqrt{1 + \sin x} - \sqrt{1 - \sin x}} \right\}\], show that \[\frac{dy}{dx}\] is independent of x. ?
If \[x y^2 = 1,\] prove that \[2\frac{dy}{dx} + y^3 = 0\] ?
Differentiate \[\left( \log x \right)^{ \log x }\] ?
Differentiate \[\sin \left( x^x \right)\] ?
Differentiate \[x^\left( \sin x - \cos x \right) + \frac{x^2 - 1}{x^2 + 1}\] ?
If `y=(sinx)^x + sin^-1 sqrtx "then find" dy/dx`
If \[xy = e^{x - y} , \text{ find } \frac{dy}{dx}\] ?
If \[y = e^{x^{e^x}} + x^{e^{e^x}} + e^{x^{x^e}}\], prove that \[\frac{dy}{dx} = e^{x^{e^x}} \cdot x^{e^x} \left\{ \frac{e^x}{x} + e^x \cdot \log x \right\}+ x^{e^{e^x}} \cdot e^{e^x} \left\{ \frac{1}{x} + e^x \cdot \log x \right\} + e^{x^{x^e}} x^{x^e} \cdot x^{e - 1} \left\{ x + e \log x \right\}\]
If \[y = \left( \cos x \right)^{\left( \cos x \right)^{\left( \cos x \right) . . . \infty}}\],prove that \[\frac{dy}{dx} = - \frac{y^2 \tan x}{\left( 1 - y \log \cos x \right)}\]?
Find \[\frac{dy}{dx}\] , when \[x = b \sin^2 \theta \text{ and } y = a \cos^2 \theta\] ?
Find \[\frac{dy}{dx}\] ,when \[x = \frac{e^t + e^{- t}}{2} \text{ and } y = \frac{e^t - e^{- t}}{2}\] ?
If \[x = a \left( \theta - \sin \theta \right) and, y = a \left( 1 + \cos \theta \right), \text { find } \frac{dy}{dx} \text{ at }\theta = \frac{\pi}{3} \] ?
If \[x = a\sin2t\left( 1 + \cos2t \right) \text { and y } = b\cos2t\left( 1 - \cos2t \right)\] , show that at \[t = \frac{\pi}{4}, \frac{dy}{dx} = \frac{b}{a}\] ?
Differentiate (log x)x with respect to log x ?
Differentiate \[\tan^{- 1} \left( \frac{1 - x}{1 + x} \right)\] with respect to \[\sqrt{1 - x^2},\text {if} - 1 < x < 1\] ?
If \[y = \sin^{- 1} x + \cos^{- 1} x\] ,find \[\frac{dy}{dx}\] ?
If \[f\left( x \right) = \log \left\{ \frac{u \left( x \right)}{v \left( x \right)} \right\}, u \left( 1 \right) = v \left( 1 \right) \text{ and }u' \left( 1 \right) = v' \left( 1 \right) = 2\] , then find the value of `f' (1)` ?
If f (x) is an odd function, then write whether `f' (x)` is even or odd ?
If \[x = 3\sin t - \sin3t, y = 3\cos t - \cos3t \text{ find }\frac{dy}{dx} \text{ at } t = \frac{\pi}{3}\] ?
If \[y = \sin^{- 1} \left( \frac{1 - x^2}{1 + x^2} \right), \text { then } \frac{dy}{dx} =\] _____________ .
\[\frac{d}{dx} \left\{ \tan^{- 1} \left( \frac{\cos x}{1 + \sin x} \right) \right\} \text { equals }\] ______________ .
Find the second order derivatives of the following function sin (log x) ?
If y = ex cos x, prove that \[\frac{d^2 y}{d x^2} = 2 e^x \cos \left( x + \frac{\pi}{2} \right)\] ?
If y = (sin−1 x)2, then (1 − x2)y2 is equal to
If xy = e(x – y), then show that `dy/dx = (y(x-1))/(x(y+1)) .`
Differentiate `log [x+2+sqrt(x^2+4x+1)]`
