What is the derivative of 3^{x^2cot(2x}) ?

The derivative of 3^{x^2cot(2x}) is ln(3)*3^{x^2cot(2x)}(2xcot(2x)-2x^2csc^2(2x))

What is the first derivative of 3^{x^2cot(2x}) ?

The first derivative of 3^{x^2cot(2x}) is ln(3)*3^{x^2cot(2x)}(2xcot(2x)-2x^2csc^2(2x))

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\frac{d}{d x} (3^{x^{2} c o t (2 x)})

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

Solution steps

\frac{d}{d x} (3^{x^{2} c o t (2 x)})

Apply exponent rule:

a^{b} = e^{b l n (a)}

3^{x^{2} c o t (2 x)} = e^{x^{2} c o t (2 x) l n (3)}

= \frac{d}{d x} (e^{x^{2} c o t (2 x) l n (3)})

Apply the chain rule:

e^{x^{2} c o t (2 x) l n (3)} \frac{d}{d x} (x^{2} cot (2 x) ln (3))

= e^{x^{2} c o t (2 x) l n (3)} \frac{d}{d x} (x^{2} cot (2 x) ln (3))

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

= e^{x^{2} c o t (2 x) l n (3)} ln (3) (2 x cot (2 x) - 2 x^{2} csc^{2} (2 x))

e^{x^{2} c o t (2 x) l n (3)} = 3^{x^{2} c o t (2 x)}

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

\frac{d}{d x} (\frac{8}{3 x})

\frac{x + 3}{x - 3}

\int 7 e^{10 x} d x

\int 4 cos (θ) d θ

\int (3 x + 1) 3 3 x^{2} + 2 x d x

What is the derivative of 3^{x^2cot(2x}) ?
The derivative of 3^{x^2cot(2x}) is ln(3)*3^{x^2cot(2x)}(2xcot(2x)-2x^2csc^2(2x))
What is the first derivative of 3^{x^2cot(2x}) ?
The first derivative of 3^{x^2cot(2x}) is ln(3)*3^{x^2cot(2x)}(2xcot(2x)-2x^2csc^2(2x))