What is the derivative of x^{sin(3x}) ?

The derivative of x^{sin(3x}) is x^{sin(3x)}(3cos(3x)ln(x)+(sin(3x))/x)

What is the first derivative of x^{sin(3x}) ?

The first derivative of x^{sin(3x}) is x^{sin(3x)}(3cos(3x)ln(x)+(sin(3x))/x)

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\frac{d}{d x} (x^{s i n (3 x)})

x^{s i n (3 x)} (3 cos (3 x) ln (x) + \frac{sin ( 3 x )}{x})

Solution steps

\frac{d}{d x} (x^{s i n (3 x)})

Apply exponent rule:

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

x^{s i n (3 x)} = e^{s i n (3 x) l n (x)}

= \frac{d}{d x} (e^{s i n (3 x) l n (x)})

Apply the chain rule:

e^{s i n (3 x) l n (x)} \frac{d}{d x} (sin (3 x) ln (x))

= e^{s i n (3 x) l n (x)} \frac{d}{d x} (sin (3 x) ln (x))

\frac{d}{d x} (sin (3 x) ln (x)) = 3 cos (3 x) ln (x) + \frac{sin ( 3 x )}{x}

= e^{s i n (3 x) l n (x)} (3 cos (3 x) ln (x) + \frac{sin ( 3 x )}{x})

e^{s i n (3 x) l n (x)} = x^{s i n (3 x)}

= x^{s i n (3 x)} (3 cos (3 x) ln (x) + \frac{sin ( 3 x )}{x})

\frac{\partial}{\partial u} (cos (u + v))

x \to - 4 + lim (\frac{1}{( x + 4 ) ^{2}})

\int \frac{arctan ( 2 x )}{1 + 4 x ^{2}} d x

\frac{1}{12 x ^{2}}, x, \frac{x}{10}

16 y^{^{''''}} + 24 y^{^{''}} + 9 y = 0

What is the derivative of x^{sin(3x}) ?
The derivative of x^{sin(3x}) is x^{sin(3x)}(3cos(3x)ln(x)+(sin(3x))/x)
What is the first derivative of x^{sin(3x}) ?
The first derivative of x^{sin(3x}) is x^{sin(3x)}(3cos(3x)ln(x)+(sin(3x))/x)