Question

what is derivative of sin(2x+5)​

Answer 1

$\huge\mathfrak{Answer:}$

$\large\underline{\sf{\blue{Given:}}}$

• We have been given a trigonometric function sin( 2x + 5 )

$\large\underline{\sf{\blue{To \: Find:}}}$

• We have to find the derivative of given trigonometric function

$\large\underline{\sf{\blue{Concept \: Used:}}}$

Chain Rule of Differentiation:

The chain rule is a formula to compute the derivative of a composite function

$\boxed{\sf{\dfrac{d}{dx} \: f(g(x))= \dfrac{d}{dx} \:f(g(x)) \times \dfrac{d}{dx} \: g(x)}}$

$\sf{}$

$\large\underline{\sf{\blue{Solution:}}}$

Given a Trigonometric function in terms of variable x

$\implies \boxed{\sf{y = sin(2x+5)}}$

$\sf{}$

$\large\underline{\mathfrak{\red{Differentiating \: the \: function}}}$

$\implies \sf{\dfrac{dy}{dx} = \dfrac{d}{dx} sin(2x+5)}$

$\implies \sf{\dfrac{dy}{dx} = cos(2x+5) \times \dfrac{d}{dx} (2x+5)}$

$\implies \sf{\dfrac{dy}{dx} = cos(2x+5) \times \left ( \dfrac{d}{dx} 2x + \dfrac{d}{dx} 5 \right ) }$

$\implies \sf{\dfrac{dy}{dx} = cos(2x+5) \times 2}$

$\implies \boxed{\sf{\dfrac{dy}{dx} = 2 \: cos(2x+5) }}$

$\sf{}$

Derivative of sin(2x + 5) is 2cos(2x + 5)

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$\large\purple{\underline{\underline{\mathtt{Some \: Derivative \: Formulas:}}}}$

• $\ \sf{\dfrac{d}{dx} sinx = cosx}$

• $\sf{\dfrac{d}{dx} cosx = - sinx}$

• $\sf{\dfrac{d}{dx} tanx = sec^2 x}$

• $\sf{\dfrac{d}{dx} (y + z)= \dfrac{dy}{dx} + \dfrac{dz}{dx}}$

• $\sf{\dfrac{d}{dx} k = 0}$, where k is constant

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