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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

\frac{d}{d x} (x sin (e^{x}))

\frac{d y}{d x} + 2 y = 3, y (0) = 1

f (x) = x^{4} + 8 x

\frac{d}{d x} (\frac{g ( x )}{h ( x )})

f (x) = 4 x - 8

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