What is the derivative of (9x)/(2^x) ?

The derivative of (9x)/(2^x) is (9(1-ln(2)x))/(2^x)

What is the first derivative of (9x)/(2^x) ?

The first derivative of (9x)/(2^x) is (9(1-ln(2)x))/(2^x)

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derivative of

\frac{9 x}{2 ^{x}}

\frac{9 ( 1 - ln ( 2 ) x )}{2 ^{x}}

Solution steps

\frac{d}{d x} (\frac{9 x}{2 ^{x}})

Take the constant out:

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

= 9 \frac{d}{d x} (\frac{x}{2 ^{x}})

Apply the Quotient Rule:

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

= 9 \cdot \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)

= 9 \cdot \frac{1 \cdot 2 ^{x} - 2 ^{x} ln ( 2 ) x}{( 2 ^{x} ) ^{2}}

Simplify

9 \cdot \frac{1 \cdot 2 ^{x} - 2 ^{x} ln ( 2 ) x}{( 2 ^{x} ) ^{2}} : \frac{9 ( 1 - ln ( 2 ) x )}{2 ^{x}}

= \frac{9 ( 1 - ln ( 2 ) x )}{2 ^{x}}

y = 4 x^{2} + 2

x \to - 2 lim (\frac{x ^{2} - 3}{x + 2})

\frac{\partial}{\partial y} (e^{x^{2} - y})

\int 3 x + \frac{10}{x ^{6}} d x

\frac{d ^{2}}{d x ^{2}} (lo g_{10} (x))

What is the derivative of (9x)/(2^x) ?
The derivative of (9x)/(2^x) is (9(1-ln(2)x))/(2^x)
What is the first derivative of (9x)/(2^x) ?
The first derivative of (9x)/(2^x) is (9(1-ln(2)x))/(2^x)