List of top Mathematics Questions on Derivatives asked in MHT CET

If \(y = cos^2[cot^{-1}(\sqrt{\frac{1-x}{1+x}})]\) then \(\frac{dy}{dx} =\) ........

If \(f(x),g(x)\) be twice differentiable functions, satisfying \(f^{''}(x) = g^{''}(x),f^'(1) = 2g^'(1) = 4\) and \(f(2) = 3g(2) = 9\) then \(f(x)-g(x)\) at \(x = 4\) is equal to

If \(\sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}} = 6\), then \(\frac{dy}{dx} =\)

If \(\sqrt{y+x}+\sqrt{y-x} = c\) and \(\frac{dy}{dx} = K-\sqrt{\frac{y^2}{x^2}-1}\) , then the value of \(K\) is

If \(y = (x^2+1)^{sinx}\) for \(x > 0\) such that \(\frac{dy}{dx} = y[\frac{2xsinx}{g(x)}+cosx\cdot log[g(x)]]\), then the function \(\frac{1}{g(x)}\) is...

The derivative of \(f(sinx)\) with respect to \(g(secx)\) at \(x = \frac{π}{4}\), given that \(f^'(\frac{1}{\sqrt{2}}) = 3\) and \(g^'(\sqrt{2}) = 1\) is.....

If \(sec^{-1}(\frac{x^2+y^2}{x^2-y^2}) = 2a\) such that \(y\frac{dy}{dx} = x\cdot f(a)\) then the value of \(f(\frac{2π}{3})\) is

If \(3y^2-2xy-x = 0\), then the value of \(\frac{dy}{dx}\) at \(y = 2\) is...

If \(y = sin^{-1}(\frac{25-x^2}{25+x^2})\), then \(y^'(1)\) is...

If \(f(x)\) and \(g(x)\) are inverse functions of each other and \(f(x) = x+e^x\), then \(g^'(x) =\)...

The derivative of \(log_{10}x\) with respect to \(log_x10\) is

If \(y = sin(2sin^{-1}x)\) then \(\frac{dy}{dx} =\)..

If \(y = cot^{-1}(\frac{1+sin5x}{cos5x})\), then the value of \(\frac{dy}{dx}\) is

If \(x\,e^{xy} = y+sin^2x\), then the value of \(\frac{dy}{dx}\) at \(x = 0\) is equal to

If \(g(x) = (x^2+2x+1)\cdot f(x)\) such that \(f(0) = 5\) and \(\underset{x\rightarrow 0}{lim}\frac{f(x)-5}{x} = 4\) then \(g^'(0) =\)

If \(f(x) = cosx\,cos2x\,cos4x\,cos8x\,cos16x\), then \(f^'(\frac{π}{4}) =\)

If \(y = \sqrt{cosx^2+\sqrt{cosx^2+\sqrt{cosx^2+\ldots \infty }}}\) and \(\frac{dy}{dx} = \frac{f(x)}{2y-1}\) then, \(\int f(x)\,dx = \ldots\)

If \(y = x\cdot 7^x\), then the value of \(\frac{dx}{dy}\) when \(x = 1\) is

If \(y = [(x+1)(2x+1)(3x+1)\ldots \ldots (nx+1)]^4\), where \(n\in N\) and \(\frac{dy}{dx}\) at \(x = 0\) is \(2k\), then the value of \(k\) is

If \(f(x) = cosxcos2xcos4xcos8xcos16x\), then \(f^'(\frac{π}{4})\) is equal to

If \(y = cos^{-1}(\frac{1-4^x}{1+4^x})\), then \(\frac{dy}{dx}\) at \(x = 1\) is

The derivative of \(log_8(log_5x)\) w. r. t. \(x\) is

The derivative of \(sin(log(\frac{x+3}{x}))\) is

If \(y = tan^{-1}\sqrt{\frac{1+sin2x}{1-sin2x}}\), then \(\frac{\text{d}y}{\text{d}x}\) at \(x = \frac{π}{6}\) is

If \(f(x) = \sqrt{x^2+1},g(x) = \frac{x+1}{x^2+1},h(x) = 2x-3\), then \(f^'(h^'(g^'(x))) =\)