What is the derivative of (x^5-16/(2^x)) ?

The derivative of (x^5-16/(2^x)) is (5x^4-ln(2)(x^5-16))/(2^x)

What is the first derivative of (x^5-16/(2^x)) ?

The first derivative of (x^5-16/(2^x)) is (5x^4-ln(2)(x^5-16))/(2^x)

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\frac{d}{d x} (\frac{x ^{5} - 16}{2 ^{x}})

\frac{5 x ^{4} - ln ( 2 ) ( x ^{5} - 16 )}{2 ^{x}}

Solution steps

\frac{d}{d x} (\frac{x ^{5} - 16}{2 ^{x}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{5} - 16 ) 2 ^{x} - \frac{d}{d x} ( 2 ^{x} ) ( x ^{5} - 16 )}{( 2 ^{x} ) ^{2}}

\frac{d}{d x} (x^{5} - 16) = 5 x^{4}

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

= \frac{5 x ^{4} \cdot 2 ^{x} - 2 ^{x} ln ( 2 ) ( x ^{5} - 16 )}{( 2 ^{x} ) ^{2}}

Simplify

\frac{5 x ^{4} \cdot 2 ^{x} - 2 ^{x} ln ( 2 ) ( x ^{5} - 16 )}{( 2 ^{x} ) ^{2}} : \frac{5 x ^{4} - ln ( 2 ) ( x ^{5} - 16 )}{2 ^{x}}

= \frac{5 x ^{4} - ln ( 2 ) ( x ^{5} - 16 )}{2 ^{x}}

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

\int 21 x^{20} d x

f (x) = \frac{2 x + 4 x ^{2}}{( 1 + 4 x ) ^{2}}

\int \frac{13}{x ^{3} - 125} d x

2 y = 4 x, 2 y + x = 5, y = 5

What is the derivative of (x^5-16/(2^x)) ?
The derivative of (x^5-16/(2^x)) is (5x^4-ln(2)(x^5-16))/(2^x)
What is the first derivative of (x^5-16/(2^x)) ?
The first derivative of (x^5-16/(2^x)) is (5x^4-ln(2)(x^5-16))/(2^x)