What is (\partial)/(\partial x)(x^{cos(x)}) ?

The answer to (\partial)/(\partial x)(x^{cos(x)}) is x^{cos(x)}(-sin(x)ln(x)+(cos(x))/x)

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(\partial)/(\partial x)(x^{cos(x)})

\frac{\partial}{\partial x} (x^{c o s (x)})

x^{c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

Solution steps

\frac{\partial}{\partial x} (x^{c o s (x)})

Apply exponent rule:

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

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

= \frac{\partial}{\partial x} (e^{c o s (x) l n (x)})

Apply the chain rule:

e^{c o s (x) l n (x)} \frac{\partial}{\partial x} (cos (x) ln (x))

= e^{c o s (x) l n (x)} \frac{\partial}{\partial x} (cos (x) ln (x))

\frac{\partial}{\partial x} (cos (x) ln (x)) = - sin (x) ln (x) + \frac{cos ( x )}{x}

= e^{c o s (x) l n (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

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

= x^{c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

e^{18 x}

x \to \infty lim (x^{(\frac{1}{x ^{2} - 1})})

\int (x^{2} - 1)^{4} d x

\frac{d}{d x} (\frac{( x + 2 )}{( x - 1 )})

x^{12}

What is (\partial)/(\partial x)(x^{cos(x)}) ?
The answer to (\partial)/(\partial x)(x^{cos(x)}) is x^{cos(x)}(-sin(x)ln(x)+(cos(x))/x)