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Popular >

derivative of x/(2^x)

Solution

\frac{d}{d x} (\frac{x}{2 ^{x}})

Solution

\frac{1 - ln ( 2 ) x}{2 ^{x}}

Solution steps

\frac{d}{d x} (\frac{x}{2 ^{x}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d x}{d x} 2 ^{x} - \frac{d}{d x} ( 2 ^{x} ) x}{( 2 ^{x} ) ^{2}}

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

\frac{d}{d x} (2^{x}) = 2^{x} ln (2)

= \frac{1 \cdot 2 ^{x} - 2 ^{x} ln ( 2 ) x}{( 2 ^{x} ) ^{2}}

Simplify

\frac{1 \cdot 2 ^{x} - 2 ^{x} ln ( 2 ) x}{( 2 ^{x} ) ^{2}} : \frac{1 - ln ( 2 ) x}{2 ^{x}}

= \frac{1 - ln ( 2 ) x}{2 ^{x}}

Popular Examples

integral from 1 to e of x^nln(x^m)

\int_{1}^{e} x^{n} ln (x^{m}) d x

(d^2)/(dx^2)(e^{6e^x})

\frac{d ^{2}}{d x ^{2}} (e^{6 e^{x}})

f(x)=x^4-4x^3-20x^2+96x+60

f (x) = x^{4} - 4 x^{3} - 20 x^{2} + 96 x + 60

y^{''}+3y^'=0,y(0)=2

y^{^{''}} + 3 y^{^{'}} = 0, y (0) = 2

integral of cos^2(xsi)n^2x

\int cos^{2} (x s i) n^{2} x d x

Frequently Asked Questions (FAQ)

What is the derivative of x/(2^x) ?
The derivative of x/(2^x) is (1-ln(2)x)/(2^x)
What is the first derivative of x/(2^x) ?
The first derivative of x/(2^x) is (1-ln(2)x)/(2^x)