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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

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