List of top Mathematics Questions on Derivatives asked in KCET

If \( y = a \sin^3 t \), \( x = a \cos^3 t \), then \( \frac{dy}{dx} \) at \( t = \frac{3\pi}{4} \) is:

The derivative of \( \sin x \) with respect to \( \log x \) is:

The function \( f(x) = \tan x - x \)

A circular plate of radius 5 cm is heated. Due to expansion, its radius increases at the rate of 0.05 cm/sec. The rate at which its area is increasing when the radius is 5.2 cm is

If \(u=\sin^{-1}(\frac{2x}{1+x^2})\) and \(v=\tan^{-1}(\frac{2x}{1-x^2})\) then \(\frac{du}{dv}\) is

Consider the following statements :
Statement 1 : If y = log₁₀x + log_ex then \(\frac{dy}{dx}=\frac{\log_{10}e}{x}+\frac{1}{x}\)
Statement 2 : \(\frac{d}{dx}(\log_{10}x)=\frac{\log x}{\log 10}\ \text{and}\ \frac{d}{dx}(\log_ex)=\frac{\log x}{\log e}\)

If y = (cosx²)², then \(\frac{dy}{dx}\) is equal to

If (xe)^y = e^x, then \(\frac{dy}{dx}\) is

The perimeter of a sector is a constant. If its area is to be maximum, then the sectorial angle is