What is the derivative of x^{sin(2x}) ?

The derivative of x^{sin(2x}) is x^{sin(2x)}(2cos(2x)ln(x)+(sin(2x))/x)

What is the first derivative of x^{sin(2x}) ?

The first derivative of x^{sin(2x}) is x^{sin(2x)}(2cos(2x)ln(x)+(sin(2x))/x)

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\frac{d}{d x} (x^{s i n (2 x)})

x^{s i n (2 x)} (2 cos (2 x) ln (x) + \frac{sin ( 2 x )}{x})

Solution steps

\frac{d}{d x} (x^{s i n (2 x)})

Apply exponent rule:

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

x^{s i n (2 x)} = e^{s i n (2 x) l n (x)}

= \frac{d}{d x} (e^{s i n (2 x) l n (x)})

Apply the chain rule:

e^{s i n (2 x) l n (x)} \frac{d}{d x} (sin (2 x) ln (x))

= e^{s i n (2 x) l n (x)} \frac{d}{d x} (sin (2 x) ln (x))

\frac{d}{d x} (sin (2 x) ln (x)) = 2 cos (2 x) ln (x) + \frac{sin ( 2 x )}{x}

= e^{s i n (2 x) l n (x)} (2 cos (2 x) ln (x) + \frac{sin ( 2 x )}{x})

e^{s i n (2 x) l n (x)} = x^{s i n (2 x)}

= x^{s i n (2 x)} (2 cos (2 x) ln (x) + \frac{sin ( 2 x )}{x})

\frac{d}{d x} (sin^{2} (x) - cos^{2} (x) sin^{2} (x))

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

f (x) = 10 x, (1, 10)

y = arccos (4 x^{2})

y = x^{2}, y = x + 2

What is the derivative of x^{sin(2x}) ?
The derivative of x^{sin(2x}) is x^{sin(2x)}(2cos(2x)ln(x)+(sin(2x))/x)
What is the first derivative of x^{sin(2x}) ?
The first derivative of x^{sin(2x}) is x^{sin(2x)}(2cos(2x)ln(x)+(sin(2x))/x)