What is the derivative of (x^2+2sqrt(x))(1-e^x) ?

The derivative of (x^2+2sqrt(x))(1-e^x) is (2x+1/(sqrt(x)))(1-e^x)-e^x(x^2+2sqrt(x))

What is the first derivative of (x^2+2sqrt(x))(1-e^x) ?

The first derivative of (x^2+2sqrt(x))(1-e^x) is (2x+1/(sqrt(x)))(1-e^x)-e^x(x^2+2sqrt(x))

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derivative of

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

(2 x + \frac{1}{x}) (1 - e^{x}) - e^{x} (x^{2} + 2 x)

Solution steps

\frac{d}{d x} ((x^{2} + 2 x) (1 - e^{x}))

Apply the Product Rule:

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

f = x^{2} + 2 x, g = 1 - e^{x}

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

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

\frac{d}{d x} (1 - e^{x}) = - e^{x}

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

Simplify

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

\frac{d}{d x} (\frac{x + 4}{x ^{3} + x - 5})

\frac{d}{d x} (ln (\frac{3 x + 1}{3 x - 1}))

8 x + x

\int \frac{x ^{6} - x}{x ^{3}} d x

\int \frac{x + 2}{x ^{2} + 7 x - 8} d x

What is the derivative of (x^2+2sqrt(x))(1-e^x) ?
The derivative of (x^2+2sqrt(x))(1-e^x) is (2x+1/(sqrt(x)))(1-e^x)-e^x(x^2+2sqrt(x))
What is the first derivative of (x^2+2sqrt(x))(1-e^x) ?
The first derivative of (x^2+2sqrt(x))(1-e^x) is (2x+1/(sqrt(x)))(1-e^x)-e^x(x^2+2sqrt(x))