Question

$\frac{d}{dx} \: (sin {x}^{2} + 5)$
find the derivative w.r to x​

Answer 1

Step-by-step explanation:

$\tt\ \frac{d}{dx} \: sin( {x}^{2} + 5) \\ \\ \tt\ \implies:cos( {x}^{2} + 5). \frac{d}{dx} ( {x}^{2} + 5) \\ \\\tt\ \implies:cos( {x}^{2} + 5) \{ \frac{d}{dx} {x}^{2} + \frac{d}{dx} 5 \} \\ \\ \tt\ \implies:cos( {x}^{2} + 5) \{ {2x}^{2 - 1} + 0 \} \\ \\\tt\ \implies: cos( {x}^{2} + 5).2x\\ \\ \boxed{\sf\ \implies: 2x.cos( {x}^{2} + 5)}$

Answer 2

Answer:

$\boxed{\bf\ \implies: 2x.cos( {x}^{2} + 5)} \: \: \ddot \smile$

Step-by-step explanation:

$\sf\ \frac{d}{dx} \: sin( {x}^{2} + 5) \\ \\ \sf\ \implies:cos( {x}^{2} + 5). \frac{d}{dx} ( {x}^{2} + 5) \\ \\\sf\ \implies:cos( {x}^{2} + 5) \{ \frac{d}{dx} {x}^{2} + \frac{d}{dx} 5 \} \\ \\ \sf\ \implies:cos( {x}^{2} + 5) \{ {2x}^{2 - 1} + 0 \} \\ \\\sf\ \implies: cos( {x}^{2} + 5).2x\\ \\ \boxed{\bf\ \implies: 2x.cos( {x}^{2} + 5)} \: \: \ddot \smile$