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Popular >

derivative of 5xe^{3x}

Solution

\frac{d}{d x} (5 x e^{3 x})

Solution

5 (e^{3 x} + 3 e^{3 x} x)

Solution steps

\frac{d}{d x} (5 x e^{3 x})

Take the constant out:

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

= 5 \frac{d}{d x} (x e^{3 x})

Apply the Product Rule:

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

f = x, g = e^{3 x}

= 5 (\frac{d x}{d x} e^{3 x} + \frac{d}{d x} (e^{3 x}) x)

\frac{d x}{d x} = 1

\frac{d}{d x} (e^{3 x}) = e^{3 x} \cdot 3

= 5 (1 \cdot e^{3 x} + e^{3 x} \cdot 3 x)

Simplify

= 5 (e^{3 x} + 3 e^{3 x} x)

Popular Examples

integral from 0 to pi/3 of 8sec^3(x)

\int_{0}^{\frac{π}{3}} 8 sec^{3} (x) d x

tangent of f(x)=sqrt(7x+2),(2,4)tangent of

f (x) = 7 x + 2, (2, 4)

xy^'+y=e^x,y(1)=1

x y^{^{'}} + y = e^{x}, y (1) = 1

slope ofintercept (3,6),(5,-8)slope intercept

(3, 6), (5, - 8)

(\partial)/(\partial x)(ln(x+t^2))

\frac{\partial}{\partial x} (ln (x + t^{2}))

Frequently Asked Questions (FAQ)

What is the derivative of 5xe^{3x} ?
The derivative of 5xe^{3x} is 5(e^{3x}+3e^{3x}x)
What is the first derivative of 5xe^{3x} ?
The first derivative of 5xe^{3x} is 5(e^{3x}+3e^{3x}x)