What is the derivative of (x^2/(2^x)) ?

The derivative of (x^2/(2^x)) is (x(2-ln(2)x))/(2^x)

What is the first derivative of (x^2/(2^x)) ?

The first derivative of (x^2/(2^x)) is (x(2-ln(2)x))/(2^x)

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int \frac{1}{x ^{2}} - 1 d x

(2 x^{2} - 4 x + 4) e^{x}

cos (x), 1

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

\frac{d y}{d x} + (\frac{1 - y ^{2}}{1 - y ^{2}})^{\frac{1}{2}} = 0

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