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Popular >

derivative of x^2sin^3(3x)

Solution

derivative of

x^{2} sin^{3} (3 x)

Solution

2 x sin^{3} (3 x) + 9 sin^{2} (3 x) cos (3 x) x^{2}

Solution steps

\frac{d}{d x} (x^{2} sin^{3} (3 x))

Apply the Product Rule:

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

f = x^{2}, g = sin^{3} (3 x)

= \frac{d}{d x} (x^{2}) sin^{3} (3 x) + \frac{d}{d x} (sin^{3} (3 x)) x^{2}

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (sin^{3} (3 x)) = 9 sin^{2} (3 x) cos (3 x)

= 2 x sin^{3} (3 x) + 9 sin^{2} (3 x) cos (3 x) x^{2}

Popular Examples

derivative of x^{10}arctan(x)derivative of

x^{10} arctan (x)

(\partial)/(\partial y)(15-5(y+3)^2)

\frac{\partial}{\partial y} (15 - 5 (y + 3)^{2})

(\partial)/(\partial x)(7x^3cos(7x^2y))

\frac{\partial}{\partial x} (7 x^{3} cos (7 x^{2} y))

(\partial)/(\partial y)(3x^4y^2+1)

\frac{\partial}{\partial y} (3 x^{4} y^{2} + 1)

integral from-2 to 3 of (22)/(x^4)

\int_{- 2}^{3} \frac{22}{x ^{4}} d x

Frequently Asked Questions (FAQ)

What is the derivative of x^2sin^3(3x) ?
The derivative of x^2sin^3(3x) is 2xsin^3(3x)+9sin^2(3x)cos(3x)x^2
What is the first derivative of x^2sin^3(3x) ?
The first derivative of x^2sin^3(3x) is 2xsin^3(3x)+9sin^2(3x)cos(3x)x^2