What is the derivative of f(x)=x^2sin(2x) ?

The derivative of f(x)=x^2sin(2x) is 2xsin(2x)+cos(2x)*2x^2

What is the first derivative of f(x)=x^2sin(2x) ?

The first derivative of f(x)=x^2sin(2x) is 2xsin(2x)+cos(2x)*2x^2

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derivative of

f (x) = x^{2} sin (2 x)

2 x sin (2 x) + cos (2 x) \cdot 2 x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

= 2 x sin (2 x) + cos (2 x) \cdot 2 x^{2}

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

y^{^{''}} - y^{^{'}} = 1

\int \frac{4 ^{x} + 1 0 ^{x}}{2 ^{x}} d x

\int \frac{1}{x ( 1 + x )} d x

\int \frac{x}{2} (x - 1)^{2} d x

What is the derivative of f(x)=x^2sin(2x) ?
The derivative of f(x)=x^2sin(2x) is 2xsin(2x)+cos(2x)*2x^2
What is the first derivative of f(x)=x^2sin(2x) ?
The first derivative of f(x)=x^2sin(2x) is 2xsin(2x)+cos(2x)*2x^2