What is the derivative of (x^2/(4^x)) ?

The derivative of (x^2/(4^x)) is 2^{1-2x}x(1-ln(2)x)

What is the first derivative of (x^2/(4^x)) ?

The first derivative of (x^2/(4^x)) is 2^{1-2x}x(1-ln(2)x)

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

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

Solution steps

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

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} ) 4 ^{x} - \frac{d}{d x} ( 4 ^{x} ) x ^{2}}{( 4 ^{x} ) ^{2}}

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

\frac{d}{d x} (4^{x}) = ln (2) \cdot 2^{2 x + 1}

= \frac{2 x \cdot 4 ^{x} - ln ( 2 ) \cdot 2 ^{2 x + 1} x ^{2}}{( 4 ^{x} ) ^{2}}

Simplify

\frac{2 x \cdot 4 ^{x} - ln ( 2 ) \cdot 2 ^{2 x + 1} x ^{2}}{( 4 ^{x} ) ^{2}} : 2^{1 - 2 x} x (1 - ln (2) x)

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

\frac{d x}{d y} + 3 x y^{3} = 0

3 y^{2} - 2 x^{2} = 6 - 2 x y, (3, 2)

y = x^{2} - 11, y = 10 x

\frac{d}{d x} (\frac{x - 3}{x + 3})

What is the derivative of (x^2/(4^x)) ?
The derivative of (x^2/(4^x)) is 2^{1-2x}x(1-ln(2)x)
What is the first derivative of (x^2/(4^x)) ?
The first derivative of (x^2/(4^x)) is 2^{1-2x}x(1-ln(2)x)