Derivatives of Polynomials and Trigonometric Functions

Differentiate $\sin 2x$

If $y=\frac{5x}{\sqrt[3]{1-x^2}}+{\sin }^2\left(2x+3\right), \text{find} \frac{dy}{dx}$

Find the derivative of $\cos 3x$

If $x=a{\cos }^3\theta$ and $y=a{\sin }^3\theta$,

Then find $\frac{dy}{dx}$

If ${\left(x+y\right)}^2=4$ then find the value of $\frac{dy}{dx}$

A curve has equation $y=2x^2+3x-2.$ The tangent to the curve at $x=4$ meets the $x-$axis at the point $A.$ Find the coordinates of point $A.$

Evaluate: $\frac{d}{dx}\left(\sqrt{\frac{1-\cos 2x}{1+\cos 2x}}\right)$

Find the derivative of $7x^2-5x+8$

A curve has equation $y=2x^2+3x-2.$ The tangent to the curve at $x=4$ meets the $x-$axis at the point $A.$ Find the coordinates of point $A.$

If $\tan \left(\frac{x+y}{x-y}\right)=k,$ then $\frac{dy}{dx}$ is equal to

If $y^{\frac{1}{m}}=x+\sqrt{1+x^2}$ then $\left(1+x^2\right)y_2+x{y}_1=?$

Let $x^2-4y+2y+1=0$ then $y\text{'}\left(1\right)=$ 

Why does the coefficient of $x^2$ responsible for the nature of the curve of the quadratic equation?

If $y=1+\frac{1}{x}+\frac{1}{x^2}+\frac{1}{x^3}+...\infty$ with $\left|x\right|>1$, then $\frac{dy}{dx}$ is

If $y={\left(secx\right)}^x+{\left(\log x\right)}^{\sqrt{x}}$ then find $\frac{dy}{dx}$

If $f\left(x\right)={\log }_e\tan \left(\frac{\mathrm{\pi }}{4}+\frac{x}{2}\right)$ prove that $f\text{'}\left(x\right)=secx$

How to differentiate $x^2\times x^4$?

If $y=\frac{3x^6}{4}+\frac{4x^3}{\sqrt{x}}-\frac{2x^{-1}}{3}+\frac{x^{-5}}{2}$ then find $\frac{dy}{dx}$.

The anti-derivative of a function of the form $\left(3x-1\right)f\left(x\right), \left(x\ne \frac{1}{3}\right)$, is given by $3x^4-\frac{13}{3}{x}^3+\frac{3}{2}{x}^2+C$, where $C$ is the constant of integration.

Find the value of $f\left(6\right)$. Show your steps.

If $\mathrm{y}=\mathrm{cosec}\left(\cot \sqrt{\mathrm{x}}\right)$ then find $\frac{dy}{dx}$.