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

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

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

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

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derivative of

y = 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}

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