What is the derivative of x^{8sin(x}) ?

The derivative of x^{8sin(x}) is 8x^{8sin(x)}(cos(x)ln(x)+(sin(x))/x)

What is the first derivative of x^{8sin(x}) ?

The first derivative of x^{8sin(x}) is 8x^{8sin(x)}(cos(x)ln(x)+(sin(x))/x)

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\frac{d}{d x} (x^{8 s i n (x)})

8 x^{8 s i n (x)} (cos (x) ln (x) + \frac{sin ( x )}{x})

Solution steps

\frac{d}{d x} (x^{8 s i n (x)})

Apply exponent rule:

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

x^{8 s i n (x)} = e^{8 s i n (x) l n (x)}

= \frac{d}{d x} (e^{8 s i n (x) l n (x)})

Apply the chain rule:

e^{8 s i n (x) l n (x)} \frac{d}{d x} (8 sin (x) ln (x))

= e^{8 s i n (x) l n (x)} \frac{d}{d x} (8 sin (x) ln (x))

\frac{d}{d x} (8 sin (x) ln (x)) = 8 (cos (x) ln (x) + \frac{sin ( x )}{x})

= e^{8 s i n (x) l n (x)} \cdot 8 (cos (x) ln (x) + \frac{sin ( x )}{x})

e^{8 s i n (x) l n (x)} = x^{8 s i n (x)}

= 8 x^{8 s i n (x)} (cos (x) ln (x) + \frac{sin ( x )}{x})

\frac{d y}{d x} = y^{4}

\frac{\partial}{\partial y} (sin (π (4 x - 6 y)))

x \to 0 lim (\frac{1}{x ^{4}})

\frac{d}{d y} (2 y^{2})

\frac{d y}{d x} + a y - b = 0

What is the derivative of x^{8sin(x}) ?
The derivative of x^{8sin(x}) is 8x^{8sin(x)}(cos(x)ln(x)+(sin(x))/x)
What is the first derivative of x^{8sin(x}) ?
The first derivative of x^{8sin(x}) is 8x^{8sin(x)}(cos(x)ln(x)+(sin(x))/x)