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Popular >

derivative of 5e^{sqrt(x)}

Solution

\frac{d}{d x} (5 e^{x})

Solution

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

Solution steps

\frac{d}{d x} (5 e^{x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} (e^{x})

Apply the chain rule:

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

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

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

= 5 e^{x} \frac{1}{2 x}

Simplify

5 e^{x} \frac{1}{2 x} : \frac{5 e ^{x}}{2 x}

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

Popular Examples

(\partial)/(\partial x)((3x^2+3x-1)(2x+3))

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

derivative of y=(x+5)(3sqrt(x)+8)derivative of

y = (x + 5) (3 x + 8)

integral of ((x+1))/((x^2+2x+2)^3)

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

(dy)/(dx)=1+y/x

\frac{d y}{d x} = 1 + \frac{y}{x}

derivative of y=log_{4}(x)+log_{4}(x^2)derivative of

y = lo g_{4} (x) + lo g_{4} (x^{2})

Frequently Asked Questions (FAQ)

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