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Popular >

derivative of e^{{g}(x}sin(x))

Solution

\frac{d}{d x} (e^{g (x)} sin (x))

Solution

e^{g (x)} \frac{d}{d x} (g (x)) sin (x) + cos (x) e^{g (x)}

Solution steps

\frac{d}{d x} (e^{g (x)} sin (x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{g (x)}, g = sin (x)

= \frac{d}{d x} (e^{g (x)}) sin (x) + \frac{d}{d x} (sin (x)) e^{g (x)}

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

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

= e^{g (x)} \frac{d}{d x} (g (x)) sin (x) + cos (x) e^{g (x)}

Popular Examples

integral from-infinity to 12 of xe^{x/4}

\int_{- \infty}^{12} x e^{\frac{x}{4}} d x

implicit (dy)/(dx),3x^2+2y^2=30 implicit derivative

\frac{d y}{d x}, 3 x^{2} + 2 y^{2} = 30

(\partial)/(\partial x)(x^3+e^y)

\frac{\partial}{\partial x} (x^{3} + e^{y})

derivative of ln(x/6)

\frac{d}{d x} (ln (\frac{x}{6}))

integral of csc(pix)cot(pix)

\int csc (π x) cot (π x) d x

Frequently Asked Questions (FAQ)

What is the derivative of e^{{g}(x}sin(x)) ?
The derivative of e^{{g}(x}sin(x)) is e^{{g}(x)} derivative of {g}(x)sin(x)+cos(x)e^{{g}(x)}
What is the first derivative of e^{{g}(x}sin(x)) ?
The first derivative of e^{{g}(x}sin(x)) is e^{{g}(x)} derivative of {g}(x)sin(x)+cos(x)e^{{g}(x)}