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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derivative of

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})

- 5 t^{2} y^{^{''}} + t y^{^{'}} + 8 y = 0

\frac{3}{x}, 12 x, \frac{1}{3} x

\int r 1 + 4 r^{2} d r

f (x) = cos (x), at x = \frac{π}{4}

x 5^{x}

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)