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

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

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

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

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

- \frac{csc ( x ) ( cot ( x ) + ln ( 2 ) )}{2 ^{x}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (csc (x)) = - cot (x) csc (x)

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

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

Simplify

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

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

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