What is the derivative of x^{9sin(x}) ?

The derivative of x^{9sin(x}) is 9x^{9sin(x)}(cos(x)ln(x)+(sin(x))/x)

What is the first derivative of x^{9sin(x}) ?

The first derivative of x^{9sin(x}) is 9x^{9sin(x)}(cos(x)ln(x)+(sin(x))/x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (x^{9 s i n (x)})

9 x^{9 s i n (x)} (cos (x) ln (x) + \frac{sin ( x )}{x})

Solution steps

\frac{d}{d x} (x^{9 s i n (x)})

Apply exponent rule:

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

x^{9 s i n (x)} = e^{9 s i n (x) l n (x)}

= \frac{d}{d x} (e^{9 s i n (x) l n (x)})

Apply the chain rule:

e^{9 s i n (x) l n (x)} \frac{d}{d x} (9 sin (x) ln (x))

= e^{9 s i n (x) l n (x)} \frac{d}{d x} (9 sin (x) ln (x))

\frac{d}{d x} (9 sin (x) ln (x)) = 9 (cos (x) ln (x) + \frac{sin ( x )}{x})

= e^{9 s i n (x) l n (x)} \cdot 9 (cos (x) ln (x) + \frac{sin ( x )}{x})

e^{9 s i n (x) l n (x)} = x^{9 s i n (x)}

= 9 x^{9 s i n (x)} (cos (x) ln (x) + \frac{sin ( x )}{x})

\int z 4 z^{2} + 8 d z

\frac{d y}{d x} = \frac{( x - 4 )}{y - 6}

y = 10 + 9 x - x^{2}, y = - 3 x + 46, [6, 15 + \frac{1}{3}]

t y^{^{'}} = t^{3} + 7 t^{3} y

\frac{d}{d x} (tan (x) + cot (x))

What is the derivative of x^{9sin(x}) ?
The derivative of x^{9sin(x}) is 9x^{9sin(x)}(cos(x)ln(x)+(sin(x))/x)
What is the first derivative of x^{9sin(x}) ?
The first derivative of x^{9sin(x}) is 9x^{9sin(x)}(cos(x)ln(x)+(sin(x))/x)