Show that the greatest integer function \(f(x)=\left\lfloor x \right\rfloor \) is not differentiable at any integer?

Differentiate the following with respect to x : y = x³ + 5x² + 3x + 7

Differentiate the following with respect to x : y = e^x + sin x + 2

Differentiate the following with respect to x : \(y=(x-{1\over x})^2\)

Differentiate the following with respect to x : y = xe^x log x

Differentiate the following with respect to x : \(y={cos \ x \over x^3}\)

Differentiate the following with respect to x : \(y={log x \ x \over e^x}\)

Differentiate the following with respect to x : Find f ' (3) and f '(5) if f(x) = |x - 4|.

Find the derivatives of the following functions with respect to corresponding independent variables: y = cosec x . cot x

Find the derivatives of the following functions with respect to corresponding independent variables: y = log₁₀ x