What is the derivative of y=x^{10cos(x)} ?

The derivative of y=x^{10cos(x)} is 10x^{10cos(x)}(-sin(x)ln(x)+(cos(x))/x)

What is the first derivative of y=x^{10cos(x)} ?

The first derivative of y=x^{10cos(x)} is 10x^{10cos(x)}(-sin(x)ln(x)+(cos(x))/x)

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derivative of

y = x^{10 c o s (x)}

10 x^{10 c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

Solution steps

\frac{d}{d x} (x^{10 c o s (x)})

Apply exponent rule:

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

x^{10 c o s (x)} = e^{10 c o s (x) l n (x)}

= \frac{d}{d x} (e^{10 c o s (x) l n (x)})

Apply the chain rule:

e^{10 c o s (x) l n (x)} \frac{d}{d x} (10 cos (x) ln (x))

= e^{10 c o s (x) l n (x)} \frac{d}{d x} (10 cos (x) ln (x))

\frac{d}{d x} (10 cos (x) ln (x)) = 10 (- sin (x) ln (x) + \frac{cos ( x )}{x})

= e^{10 c o s (x) l n (x)} \cdot 10 (- sin (x) ln (x) + \frac{cos ( x )}{x})

e^{10 c o s (x) l n (x)} = x^{10 c o s (x)}

= 10 x^{10 c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

y = 4 tan (x), at x = \frac{π}{6}

\int_{1}^{3} (x^{2} + 1)^{3} x d x

\int_{2}^{4} \frac{1}{( x - 4 ) ( x - 1 )} d x

\int_{9}^{16} \frac{1}{2 - x} d x

\frac{\partial}{\partial y} (sin (y) + y, x)

What is the derivative of y=x^{10cos(x)} ?
The derivative of y=x^{10cos(x)} is 10x^{10cos(x)}(-sin(x)ln(x)+(cos(x))/x)
What is the first derivative of y=x^{10cos(x)} ?
The first derivative of y=x^{10cos(x)} is 10x^{10cos(x)}(-sin(x)ln(x)+(cos(x))/x)