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

The derivative of (3^x/(tan(x))) is ln(3)*3^xcot(x)-3^xcsc^2(x)

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

The first derivative of (3^x/(tan(x))) is ln(3)*3^xcot(x)-3^xcsc^2(x)

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\frac{d}{d x} (\frac{3 ^{x}}{tan ( x )})

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

Solution steps

\frac{d}{d x} (\frac{3 ^{x}}{tan ( x )})

Simplify

\frac{3 ^{x}}{tan ( x )} : 3^{x} cot (x)

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 3^{x}, g = cot (x)

= \frac{d}{d x} (3^{x}) cot (x) + \frac{d}{d x} (cot (x)) 3^{x}

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

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

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

Simplify

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

What is the derivative of (3^x/(tan(x))) ?
The derivative of (3^x/(tan(x))) is ln(3)*3^xcot(x)-3^xcsc^2(x)
What is the first derivative of (3^x/(tan(x))) ?
The first derivative of (3^x/(tan(x))) is ln(3)*3^xcot(x)-3^xcsc^2(x)