What is the derivative of x^4*sin(x*sin(3x)) ?

The derivative of x^4*sin(x*sin(3x)) is 4x^3sin(x)sin(3x)+(cos(x)sin(3x)+cos(3x)*3sin(x))x^4

What is the first derivative of x^4*sin(x*sin(3x)) ?

The first derivative of x^4*sin(x*sin(3x)) is 4x^3sin(x)sin(3x)+(cos(x)sin(3x)+cos(3x)*3sin(x))x^4

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\frac{d}{d x} (x^{4} \cdot sin (x) \cdot sin (3 x))

4 x^{3} sin (x) sin (3 x) + (cos (x) sin (3 x) + cos (3 x) \cdot 3 sin (x)) x^{4}

Solution steps

\frac{d}{d x} (x^{4} sin (x) sin (3 x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{4}, g = sin (x) sin (3 x)

= \frac{d}{d x} (x^{4}) sin (x) sin (3 x) + \frac{d}{d x} (sin (x) sin (3 x)) x^{4}

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

= 4 x^{3} sin (x) sin (3 x) + (cos (x) sin (3 x) + cos (3 x) \cdot 3 sin (x)) x^{4}

What is the derivative of x^4*sin(x*sin(3x)) ?
The derivative of x^4*sin(x*sin(3x)) is 4x^3sin(x)sin(3x)+(cos(x)sin(3x)+cos(3x)*3sin(x))x^4
What is the first derivative of x^4*sin(x*sin(3x)) ?
The first derivative of x^4*sin(x*sin(3x)) is 4x^3sin(x)sin(3x)+(cos(x)sin(3x)+cos(3x)*3sin(x))x^4