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

The derivative of x^{cos(x}) is x^{cos(x)}(-sin(x)ln(x)+(cos(x))/x)

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

The first derivative of x^{cos(x}) is x^{cos(x)}(-sin(x)ln(x)+(cos(x))/x)

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d 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})

\frac{\partial}{\partial x} (sin (- 3 x) cos (6 y))

\frac{d}{d x} ((cos (x))^{5})

x \to 0 lim (arcsin (x))

\frac{d}{d x} (lo g_{2} (x^{2} - 9 x))

\frac{d}{d x} ((x^{2} - 1) (x^{2} - 4) (x^{2} - 9))

What is the derivative of x^{cos(x}) ?
The derivative of x^{cos(x}) is x^{cos(x)}(-sin(x)ln(x)+(cos(x))/x)
What is the first derivative of x^{cos(x}) ?
The first derivative of x^{cos(x}) is x^{cos(x)}(-sin(x)ln(x)+(cos(x))/x)