What is the derivative of (2csc(x)/(3^x)) ?

The derivative of (2csc(x)/(3^x)) is -(2csc(x)(cot(x)+ln(3)))/(3^x)

What is the first derivative of (2csc(x)/(3^x)) ?

The first derivative of (2csc(x)/(3^x)) is -(2csc(x)(cot(x)+ln(3)))/(3^x)

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\frac{d}{d x} (\frac{2 csc ( x )}{3 ^{x}})

- \frac{2 csc ( x ) ( cot ( x ) + ln ( 3 ) )}{3 ^{x}}

Solution steps

\frac{d}{d x} (\frac{2 csc ( x )}{3 ^{x}})

Take the constant out:

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

= 2 \frac{d}{d x} (\frac{csc ( x )}{3 ^{x}})

Apply the Quotient Rule:

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

= 2 \cdot \frac{\frac{d}{d x} ( csc ( x ) ) 3 ^{x} - \frac{d}{d x} ( 3 ^{x} ) csc ( x )}{( 3 ^{x} ) ^{2}}

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

\frac{d}{d x} (3^{x}) = 3^{x} ln (3)

= 2 \cdot \frac{( - cot ( x ) csc ( x ) ) \cdot 3 ^{x} - 3 ^{x} ln ( 3 ) csc ( x )}{( 3 ^{x} ) ^{2}}

Simplify

2 \cdot \frac{( - cot ( x ) csc ( x ) ) \cdot 3 ^{x} - 3 ^{x} ln ( 3 ) csc ( x )}{( 3 ^{x} ) ^{2}} : - \frac{2 csc ( x ) ( cot ( x ) + ln ( 3 ) )}{3 ^{x}}

= - \frac{2 csc ( x ) ( cot ( x ) + ln ( 3 ) )}{3 ^{x}}

f (x) = - sin (x)

\int sin (\frac{π x}{12}) d x

\frac{d}{d x} (\frac{5 x ^{3} + 5 x ^{2}}{x})

\frac{\partial}{\partial x} (x^{3} - 3 x + 3 x y^{2})

x^{2} 25 - x^{2}

What is the derivative of (2csc(x)/(3^x)) ?
The derivative of (2csc(x)/(3^x)) is -(2csc(x)(cot(x)+ln(3)))/(3^x)
What is the first derivative of (2csc(x)/(3^x)) ?
The first derivative of (2csc(x)/(3^x)) is -(2csc(x)(cot(x)+ln(3)))/(3^x)