Question Type 3: The derivatives of simple composites of inverse trigonometric functions Exercises

Compute the derivative of $y=\dfrac{\arcsin(3x)}{x}\,$.

Compute the derivative of $y=\arcsin(\sqrt{x})$.

Differentiate $y=\arctan(4x+1)$.

Find $\dfrac{d}{dx}\bigl[\arccos(e^x)\bigr]\,$.

Differentiate $y=\arctan(x^2)$.

Compute $\dfrac{d}{dx}\bigl[\arccos(x^3)\bigr]\,$.

Find $\displaystyle\frac{d}{dx}\bigl[\arcsin(3x)\bigr]$.

Differentiate $y=\bigl[\arctan(5x)\bigr]^2$.

Find the derivative of $f(x) = 5 \arcsin(5x^2)$.

Find $\dfrac{d}{dx}\bigl[2\arcsin(x)+\arctan(3x)\bigr]\,$.

Find $\dfrac{d}{dx}\bigl[3\,\arccos(2x-1)\bigr]$.

Find $\dfrac{d}{dx}\bigl[\sqrt{\arcsin(x)}\bigr]$.

Compute $\dfrac{d}{dx}\bigl[\arcsin(x^2-1)\bigr]\,$.

Differentiate $y=\arctan(\sin x)$.

Differentiate $f(x)=\arctan(x)+\arcsin(x)$.