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

The derivative of (e^x(x+xsqrt(x))) is e^x(x+x^{3/2})+(1+(3sqrt(x))/2)e^x

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

The first derivative of (e^x(x+xsqrt(x))) is e^x(x+x^{3/2})+(1+(3sqrt(x))/2)e^x

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

e^{x} (x + x^{\frac{3}{2}}) + (1 + \frac{3 x}{2}) e^{x}

Solution steps

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

Simplify

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

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

Apply the Product Rule:

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

f = e^{x}, g = x + x^{\frac{3}{2}}

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

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

\frac{d}{d x} (x + x^{\frac{3}{2}}) = 1 + \frac{3 x}{2}

= e^{x} (x + x^{\frac{3}{2}}) + (1 + \frac{3 x}{2}) e^{x}

x \to 1 lim (2 x^{2} - 5 x + 1)

\int \frac{x ^{2}}{x ^{2} + 25} d x

\frac{\partial}{\partial x} (x y^{2})

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

\int (\frac{3 - x}{x ^{2} + 1} + x ln (x^{2})) d x

What is the derivative of (e^x(x+xsqrt(x))) ?
The derivative of (e^x(x+xsqrt(x))) is e^x(x+x^{3/2})+(1+(3sqrt(x))/2)e^x
What is the first derivative of (e^x(x+xsqrt(x))) ?
The first derivative of (e^x(x+xsqrt(x))) is e^x(x+x^{3/2})+(1+(3sqrt(x))/2)e^x