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Popular >

derivative of 5e^xsin(x)

Solution

\frac{d}{d x} (5 e^{x} sin (x))

Solution

5 (e^{x} sin (x) + cos (x) e^{x})

Solution steps

\frac{d}{d x} (5 e^{x} sin (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} (e^{x} sin (x))

Apply the Product Rule:

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

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

= 5 (\frac{d}{d x} (e^{x}) sin (x) + \frac{d}{d x} (sin (x)) e^{x})

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

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

= 5 (e^{x} sin (x) + cos (x) e^{x})

Popular Examples

derivative of s(t)=t^3-5t^2-3t+8 derivative of

s (t) = t^{3} - 5 t^{2} - 3 t + 8

(dy)/(dx)+y/x =2x^6y^2

\frac{d y}{d x} + \frac{y}{x} = 2 x^{6} y^{2}

derivative of f(x)=x^2*e^{-x^2}derivative of

f (x) = x^{2} \cdot e^{- x^{2}}

f (x) = \frac{50}{x}

integral of y^{4/3}

\int y^{\frac{4}{3}} d y

Frequently Asked Questions (FAQ)

What is the derivative of 5e^xsin(x) ?
The derivative of 5e^xsin(x) is 5(e^xsin(x)+cos(x)e^x)
What is the first derivative of 5e^xsin(x) ?
The first derivative of 5e^xsin(x) is 5(e^xsin(x)+cos(x)e^x)