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

The derivative of (x^2+e^x)(sqrt(x)) is (5x^2+2e^xx+e^x)/(2sqrt(x))

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

The first derivative of (x^2+e^x)(sqrt(x)) is (5x^2+2e^xx+e^x)/(2sqrt(x))

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\int \frac{x ^{2} + 60 x + 60}{x ^{3} - 4 x} d x

n = 1 \sum \infty (- 0.3)^{n - 1}

x \to 3 + lim (\frac{5 x}{x ^{2} - 9})

\frac{d}{d x} (ln (cosh (2 x)))

\frac{d}{d x} (sin (x) + \frac{7}{4} cot (x))

What is the derivative of (x^2+e^x)(sqrt(x)) ?
The derivative of (x^2+e^x)(sqrt(x)) is (5x^2+2e^xx+e^x)/(2sqrt(x))
What is the first derivative of (x^2+e^x)(sqrt(x)) ?
The first derivative of (x^2+e^x)(sqrt(x)) is (5x^2+2e^xx+e^x)/(2sqrt(x))