Use Trigonometric Differentiation: the derivative of \(\sin{x}\) is \(\cos{x}\).. \[4\cos{x}\] Done

Quotient Rule | Math Solver - Cymath ... \\"This

The Definition of Natural Logarithm Rule states that: \({e}^{y}=x\) if and only if \(\ln{x}=y\) Examples

Sum Rule | Math Solver - Cymath ... \\"This

Use Product Rule to find the derivative of \({x}^{2}\sin{x}\). The product rule states that \((fg)'=f'g+fg'\).

\(\sin^{2}x=\frac{1-\cos{2x}}{2}\) \(\cos^{2}x=\frac{1+\cos{2x}}{2}\) \(\tan{\frac{x}{2}}=\frac{\sin{x}}{1+\cos{x}}=\frac{1-\cos{x}}{\sin{x}}\)

The Square of Difference Rule states that: \({(a-b)}^{2}={a}^{2}-2ab+{b}^{2}\) Examples

Inverse Trigonometric Differentiation | Math Solver - Cymath ... \\"This

The Power Rule states that: \({({x}^{a})}^{b}={x}^{ab}\) Examples

\(\sin{x}+\sin{y}=2\sin{(\frac{x+y}{2})}\cos{(\frac{x-y}{2})}\) \(\sin{x}-\sin{y}=2\cos{(\frac{x+y}{2})}\sin{(\frac{x-y}{2})}\)