What is the derivative of (7x)/(2^x) ?

The derivative of (7x)/(2^x) is (7(1-ln(2)x))/(2^x)

What is the first derivative of (7x)/(2^x) ?

The first derivative of (7x)/(2^x) is (7(1-ln(2)x))/(2^x)

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derivative of

\frac{7 x}{2 ^{x}}

\frac{7 ( 1 - ln ( 2 ) x )}{2 ^{x}}

Solution steps

\frac{d}{d x} (\frac{7 x}{2 ^{x}})

Take the constant out:

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

= 7 \frac{d}{d x} (\frac{x}{2 ^{x}})

Apply the Quotient Rule:

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

= 7 \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)

= 7 \cdot \frac{1 \cdot 2 ^{x} - 2 ^{x} ln ( 2 ) x}{( 2 ^{x} ) ^{2}}

Simplify

7 \cdot \frac{1 \cdot 2 ^{x} - 2 ^{x} ln ( 2 ) x}{( 2 ^{x} ) ^{2}} : \frac{7 ( 1 - ln ( 2 ) x )}{2 ^{x}}

= \frac{7 ( 1 - ln ( 2 ) x )}{2 ^{x}}

(- 8, - 4), (- 6, - 1)

y = \frac{4}{3} x + 2

x \to \infty lim (\frac{+ x - 2 ^{+ x}}{3 ^{x} - 5})

\int 5 \frac{cos ( x ) + sin ( x )}{sin ( 2 x )} d x

f (x) = \frac{x}{x ^{2} + 81}

What is the derivative of (7x)/(2^x) ?
The derivative of (7x)/(2^x) is (7(1-ln(2)x))/(2^x)
What is the first derivative of (7x)/(2^x) ?
The first derivative of (7x)/(2^x) is (7(1-ln(2)x))/(2^x)