Question

Differentiate with respect to x : y =e^xsinx

e^x(sinx+cosx)
e^xcosx
exsinx+cosx
sin^2x+cosx

Answer 1

Answer on Question #46581 – Math – Differential Calculus | Equations

Differentiate with respect to

$$y = e ^ {x} \sin x$$

Solution:

Find derivative using

The Product Rule

$$\frac {d}{d x} (u \cdot v) = u \cdot \frac {d v}{d x} + v \cdot \frac {d u}{d x}$$

Let $u = e^{x}$ and $v = \sin x$ , then

$$\frac {d u}{d x} = \frac {d}{d x} e ^ {x} = e ^ {x},$$ $$\frac {d v}{d x} = \frac {d}{d x} \sin x = \cos x,$$ $$y ^ {\prime} = \frac {d}{d x} (e ^ {x} \sin x) = e ^ {x} \cos x + e ^ {x} \sin x = e ^ {x} (\cos x + \sin x)$$

Answer:

$$y ^ {\prime} = e ^ {x} (\cos x + \sin x)$$

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