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

The derivative of x^{xcos(x}) is x^{xcos(x)}(cos(x)ln(x)-xsin(x)ln(x)+cos(x))

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

The first derivative of x^{xcos(x}) is x^{xcos(x)}(cos(x)ln(x)-xsin(x)ln(x)+cos(x))

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

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

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