What is the derivative of f(x)=x^2sin(4x^2) ?

The derivative of f(x)=x^2sin(4x^2) is 2xsin(4x^2)+8x^3cos(4x^2)

What is the first derivative of f(x)=x^2sin(4x^2) ?

The first derivative of f(x)=x^2sin(4x^2) is 2xsin(4x^2)+8x^3cos(4x^2)

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derivative of

f (x) = x^{2} sin (4 x^{2})

2 x sin (4 x^{2}) + 8 x^{3} cos (4 x^{2})

Solution steps

\frac{d}{d x} (x^{2} sin (4 x^{2}))

Apply the Product Rule:

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

f = x^{2}, g = sin (4 x^{2})

= \frac{d}{d x} (x^{2}) sin (4 x^{2}) + \frac{d}{d x} (sin (4 x^{2})) x^{2}

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

\frac{d}{d x} (sin (4 x^{2})) = cos (4 x^{2}) \cdot 8 x

= 2 x sin (4 x^{2}) + cos (4 x^{2}) \cdot 8 x x^{2}

cos (4 x^{2}) \cdot 8 x x^{2} = 8 x^{3} cos (4 x^{2})

= 2 x sin (4 x^{2}) + 8 x^{3} cos (4 x^{2})

What is the derivative of f(x)=x^2sin(4x^2) ?
The derivative of f(x)=x^2sin(4x^2) is 2xsin(4x^2)+8x^3cos(4x^2)
What is the first derivative of f(x)=x^2sin(4x^2) ?
The first derivative of f(x)=x^2sin(4x^2) is 2xsin(4x^2)+8x^3cos(4x^2)