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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\frac{d}{d x} (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{2}{1 + x ^{2}}

y^{^{'}} + y = e^{3 x}

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

\int \frac{1}{csc ^{4} ( 3 x ) sec ^{2} ( 3 x )} d x

\frac{\partial}{\partial y} (3 x y e^{- x^{2} - y^{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)