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Popular >

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

Solution

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

Solution

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

Solution steps

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

Simplify

e^{2 x + l n (x)} : e^{2 x} x

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Popular Examples

derivative of (x^2-x-2)/(x^2+x-6)derivative of

\frac{x ^{2} - x - 2}{x ^{2} + x - 6}

y^{''}-8y^'+9y=0

y^{^{''}} - 8 y^{^{'}} + 9 y = 0

limit as x approaches 4 of (x^2-4)/(x-4)

x \to 4 lim (\frac{x ^{2} - 4}{x - 4})

(\partial)/(\partial y)(x/y-y/z)

\frac{\partial}{\partial y} (\frac{x}{y} - \frac{y}{z})

derivative of e^{-2x}sin(3x)

\frac{d}{d x} (e^{- 2 x} sin (3 x))

Frequently Asked Questions (FAQ)

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