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Popular >

derivative of 12sqrt(x)e^x

Solution

derivative of

12 x e^{x}

Solution

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

Solution steps

\frac{d}{d x} (12 x e^{x})

Take the constant out:

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

= 12 \frac{d}{d x} (x e^{x})

Apply the Product Rule:

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

f = x, g = e^{x}

= 12 (\frac{d}{d x} (x) e^{x} + \frac{d}{d x} (e^{x}) x)

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

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

= 12 (\frac{1}{2 x} e^{x} + e^{x} x)

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

= 12 (\frac{e ^{x}}{2 x} + e^{x} x)

Popular Examples

limit as x approaches infinity of 1+2+3

x \to \infty lim (1 + 2 + 3)

(3x+3xy+3xy^2)dx+(x^2+2x^2y)dy=0

(3 x + 3 x y + 3 x y^{2}) d x + (x^{2} + 2 x^{2} y) d y = 0

16 y^{^{''}} + 5 y = 0

derivative of sqrt(t^3-t)derivative of

t^{3} - t

derivative of (x^5-16/(2^x))

\frac{d}{d x} (\frac{x ^{5} - 16}{2 ^{x}})

Frequently Asked Questions (FAQ)

What is the derivative of 12sqrt(x)e^x ?
The derivative of 12sqrt(x)e^x is 12((e^x)/(2sqrt(x))+e^xsqrt(x))
What is the first derivative of 12sqrt(x)e^x ?
The first derivative of 12sqrt(x)e^x is 12((e^x)/(2sqrt(x))+e^xsqrt(x))