What is the derivative of x^{cos(4x)} ?

The derivative of x^{cos(4x)} is x^{cos(4x)}(-4sin(4x)ln(x)+(cos(4x))/x)

What is the first derivative of x^{cos(4x)} ?

The first derivative of x^{cos(4x)} is x^{cos(4x)}(-4sin(4x)ln(x)+(cos(4x))/x)

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derivative of

x^{c o s (4 x)}

x^{c o s (4 x)} (- 4 sin (4 x) ln (x) + \frac{cos ( 4 x )}{x})

Solution steps

\frac{d}{d x} (x^{c o s (4 x)})

Apply exponent rule:

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

x^{c o s (4 x)} = e^{c o s (4 x) l n (x)}

= \frac{d}{d x} (e^{c o s (4 x) l n (x)})

Apply the chain rule:

e^{c o s (4 x) l n (x)} \frac{d}{d x} (cos (4 x) ln (x))

= e^{c o s (4 x) l n (x)} \frac{d}{d x} (cos (4 x) ln (x))

\frac{d}{d x} (cos (4 x) ln (x)) = - 4 sin (4 x) ln (x) + \frac{cos ( 4 x )}{x}

= e^{c o s (4 x) l n (x)} (- 4 sin (4 x) ln (x) + \frac{cos ( 4 x )}{x})

e^{c o s (4 x) l n (x)} = x^{c o s (4 x)}

= x^{c o s (4 x)} (- 4 sin (4 x) ln (x) + \frac{cos ( 4 x )}{x})

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\frac{\partial}{\partial y} (x^{9 y})

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What is the derivative of x^{cos(4x)} ?
The derivative of x^{cos(4x)} is x^{cos(4x)}(-4sin(4x)ln(x)+(cos(4x))/x)
What is the first derivative of x^{cos(4x)} ?
The first derivative of x^{cos(4x)} is x^{cos(4x)}(-4sin(4x)ln(x)+(cos(4x))/x)