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

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

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

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

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derivative of

y = 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{\partial}{\partial x} (x^{2} + x e^{2} y - y)

\frac{d}{d x} (\frac{( x + 1 ) ^{5}}{( 1 - x ) ^{4}})

y = ln (e^{3 x})

x \to 49 lim (\frac{x ^{2}}{7} - \frac{7}{x})

\frac{\partial}{\partial y} (\frac{x + y}{2})

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