What is the derivative of e^x+x-3/2 e^{2x}+e^{2x}x ?

The derivative of e^x+x-3/2 e^{2x}+e^{2x}x is 2e^{2x}x+e^x-2e^{2x}+1

What is the first derivative of e^x+x-3/2 e^{2x}+e^{2x}x ?

The first derivative of e^x+x-3/2 e^{2x}+e^{2x}x is 2e^{2x}x+e^x-2e^{2x}+1

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

2 e^{2 x} x + e^{x} - 2 e^{2 x} + 1

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

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

= e^{x} + 1 - 3 e^{2 x} + 2 e^{2 x} x + e^{2 x}

Simplify

= 2 e^{2 x} x + e^{x} - 2 e^{2 x} + 1

\int cot (\frac{x}{7}) d x

\frac{d}{d x} (2 x - 4)

2^{2^{n}}

\int \frac{1}{x ^{2} a ^{2} + x ^{2}} d x

e^{- t}

What is the derivative of e^x+x-3/2 e^{2x}+e^{2x}x ?
The derivative of e^x+x-3/2 e^{2x}+e^{2x}x is 2e^{2x}x+e^x-2e^{2x}+1
What is the first derivative of e^x+x-3/2 e^{2x}+e^{2x}x ?
The first derivative of e^x+x-3/2 e^{2x}+e^{2x}x is 2e^{2x}x+e^x-2e^{2x}+1