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Popular >

derivative of f(x)=e^xsqrt(x)

Solution

derivative of

f (x) = e^{x} x

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = e^{x}, g = x

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

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

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

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

\frac{1}{2 x} e^{x} = \frac{e ^{x}}{2 x}

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

Graph

Popular Examples

area y=8cos(3x),y=8sin(3x),(0, pi/(12))area

y = 8 cos (3 x), y = 8 sin (3 x), (0, \frac{π}{12})

tangent of f(x)= 5/(sqrt(x)),(1,5)tangent of

f (x) = \frac{5}{x}, (1, 5)

derivative of (x^2+x^3^4)

\frac{d}{d x} ((x^{2} + x^{3})^{4})

(\partial)/(\partial x)(x*y^2*e^z)

\frac{\partial}{\partial x} (x \cdot y^{2} \cdot e^{z})

derivative of y=cos^3(pit-16)derivative of

y = cos^{3} (π t - 16)

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=e^xsqrt(x) ?
The derivative of f(x)=e^xsqrt(x) is e^xsqrt(x)+(e^x)/(2sqrt(x))
What is the first derivative of f(x)=e^xsqrt(x) ?
The first derivative of f(x)=e^xsqrt(x) is e^xsqrt(x)+(e^x)/(2sqrt(x))