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

The derivative of y=x^2sin(4x) is 2xsin(4x)+cos(4x)*4x^2

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

The first derivative of y=x^2sin(4x) is 2xsin(4x)+cos(4x)*4x^2

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

f (x) = x^{2} + x, at x = 4

y^{^{''}} + 4 y^{^{'}} + 4 y = 0, y (0) = 0, y^{^{'}} (0) = 1

\frac{d}{d x} (\frac{- 6 x}{x ^{2} + 1})

9 x^{2} y^{^{'}} = y^{^{'}} + 5 x e^{- y}

\frac{d y}{d x} = x \cdot e^{- 2 x}

What is the derivative of y=x^2sin(4x) ?
The derivative of y=x^2sin(4x) is 2xsin(4x)+cos(4x)*4x^2
What is the first derivative of y=x^2sin(4x) ?
The first derivative of y=x^2sin(4x) is 2xsin(4x)+cos(4x)*4x^2