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Popular >

derivative of (x+2e^{2x})

Solution

\frac{d}{d x} ((x + 2) e^{2 x})

Solution

2 e^{2 x} x + 5 e^{2 x}

Solution steps

\frac{d}{d x} ((x + 2) e^{2 x})

Apply the Product Rule:

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

f = x + 2, g = e^{2 x}

= \frac{d}{d x} (x + 2) e^{2 x} + \frac{d}{d x} (e^{2 x}) (x + 2)

\frac{d}{d x} (x + 2) = 1

\frac{d}{d x} (e^{2 x}) = e^{2 x} \cdot 2

= 1 \cdot e^{2 x} + e^{2 x} \cdot 2 (x + 2)

Simplify

1 \cdot e^{2 x} + e^{2 x} \cdot 2 (x + 2) : 2 e^{2 x} x + 5 e^{2 x}

= 2 e^{2 x} x + 5 e^{2 x}

Popular Examples

(\partial)/(\partial x)(xln(y)+y^2z+z^2)

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

derivative of f(x)=6x-3 derivative of

f (x) = 6 x - 3

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

\frac{d x}{d y} = \frac{2 y + sec ^{2} ( y )}{2 x}

(3 e^{x})^{^{'}}

integral from 0 to 0.5 of 250x

\int_{0}^{0.5} 250 x d x

Frequently Asked Questions (FAQ)

What is the derivative of (x+2e^{2x}) ?
The derivative of (x+2e^{2x}) is 2e^{2x}x+5e^{2x}
What is the first derivative of (x+2e^{2x}) ?
The first derivative of (x+2e^{2x}) is 2e^{2x}x+5e^{2x}