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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

\int e^{y t} \cdot sin (k t) d t

(2 t)^{^{'}}

\int \frac{1}{x ^{2} - 4 x + 13} d x

\frac{d}{d x} (e^{x} sin (x) cos^{3} (x))

\int (\frac{x ^{2}}{5 + 2 x ^{3}}) d x

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