What is the derivative of x^{6cos(x)} ?

The derivative of x^{6cos(x)} is 6x^{6cos(x)}(-sin(x)ln(x)+(cos(x))/x)

What is the first derivative of x^{6cos(x)} ?

The first derivative of x^{6cos(x)} is 6x^{6cos(x)}(-sin(x)ln(x)+(cos(x))/x)

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derivative of

x^{6 c o s (x)}

6 x^{6 c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

Solution steps

\frac{d}{d x} (x^{6 c o s (x)})

Apply exponent rule:

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

x^{6 c o s (x)} = e^{6 c o s (x) l n (x)}

= \frac{d}{d x} (e^{6 c o s (x) l n (x)})

Apply the chain rule:

e^{6 c o s (x) l n (x)} \frac{d}{d x} (6 cos (x) ln (x))

= e^{6 c o s (x) l n (x)} \frac{d}{d x} (6 cos (x) ln (x))

\frac{d}{d x} (6 cos (x) ln (x)) = 6 (- sin (x) ln (x) + \frac{cos ( x )}{x})

= e^{6 c o s (x) l n (x)} \cdot 6 (- sin (x) ln (x) + \frac{cos ( x )}{x})

e^{6 c o s (x) l n (x)} = x^{6 c o s (x)}

= 6 x^{6 c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

\frac{d}{d x} (8^{x^{4}})

\frac{x}{1 + x ^{2}}, \frac{x ^{2}}{1 + x ^{3}}, [0, 1]

\int \frac{8}{4 + 8 x} d x

\frac{180}{x ^{7}} - \frac{4}{x ^{3}}

\frac{d y}{d x} = (e^{x} - e^{- x})^{2}

What is the derivative of x^{6cos(x)} ?
The derivative of x^{6cos(x)} is 6x^{6cos(x)}(-sin(x)ln(x)+(cos(x))/x)
What is the first derivative of x^{6cos(x)} ?
The first derivative of x^{6cos(x)} is 6x^{6cos(x)}(-sin(x)ln(x)+(cos(x))/x)