Differentiate the following: \(f(x)=\frac{x}{\sqrt{7-3 x}}\)

Differentiate the following: \(y=5^{\frac{-1}{x}}\)

Differentiate the following: y = sin³ x + cos³ x

Find f'(x) if f(x) = cos^-1(4x³ - 3x).

Find \({dy\over dx}\) if x = at² ; y = 2at, t\(\neq 0.\)

Find \({dy\over dx}\) if x = a(t - sin t), y = a(1 - cos t).

Find y', y''and y''' if y = x³ - 6x² - 5x + 3.

Find f'' if f(x) = x cos x.

Find the derivatives of the following : x = a cos³ t; y = a sin³ t

Find the derivative of sin x² with respect to x².