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

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

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

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

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derivative of

f (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})

n \to \infty lim (- 1 0^{n})

x \to - 3 lim (\frac{x}{x + 5})

\frac{d}{d x} ((x^{2} - 3)^{3})

\int \frac{14}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x

\int ln (x^{6}) d x

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