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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

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