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Nefissi8u

Answered question

2021-12-01

Find the derivatives of the function defined as follows.

y = - 3 e^{2} \sin x

Answer & Explanation

rerCessbalmuh

Beginner2021-12-02Added 13 answers

Step 1:Given
The function:

y = - 3 e^{2} \sin x

Step 2:Formula used

\frac{d}{d x} (e^{x}) = e^{x}

\frac{d}{d x} (\sin x) = - \cos x

Step 3:Solution
Consider the given function:

y = - 3 e^{2 \sin x}

Differentiating both sides with respect to x, we get,

\frac{d y}{d x} = \frac{d}{d x} (- 3 e^{2 \sin x})

\Rightarrow \frac{d y}{d x} = - 3 \frac{d}{d x} (e^{2 \sin x})

Using chain rule, we get,

\Rightarrow \frac{d y}{d x} = - 3 e^{2 \sin x} \cdot \frac{d}{d x} (\sin x)

\Rightarrow \frac{d y}{d x} = - 3 e^{2 \sin x} (\cos x)

\Rightarrow \frac{d y}{d x} = - 3 \cos x e^{2 \sin x}

Step 4:Conclusion
Hence,

\frac{d y}{d x} = - 3 \cos x e^{2 \sin x}

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