What is the derivative of x^2sin(5x) ?

The derivative of x^2sin(5x) is 2xsin(5x)+cos(5x)*5x^2

What is the first derivative of x^2sin(5x) ?

The first derivative of x^2sin(5x) is 2xsin(5x)+cos(5x)*5x^2

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derivative of

x^{2} sin (5 x)

2 x sin (5 x) + cos (5 x) \cdot 5 x^{2}

Solution steps

\frac{d}{d x} (x^{2} sin (5 x))

Apply the Product Rule:

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

f = x^{2}, g = sin (5 x)

= \frac{d}{d x} (x^{2}) sin (5 x) + \frac{d}{d x} (sin (5 x)) x^{2}

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

\frac{d}{d x} (sin (5 x)) = cos (5 x) \cdot 5

= 2 x sin (5 x) + cos (5 x) \cdot 5 x^{2}

\frac{d y}{d x} = \frac{( x - 4 )}{y + 5}

\frac{t}{2 t + 3}

\int cos^{3} (4 θ) sin (4 θ) d θ

\frac{d y}{d x} = - x e^{- x + y}

y^{^{'}} = y (2 + y) t

What is the derivative of x^2sin(5x) ?
The derivative of x^2sin(5x) is 2xsin(5x)+cos(5x)*5x^2
What is the first derivative of x^2sin(5x) ?
The first derivative of x^2sin(5x) is 2xsin(5x)+cos(5x)*5x^2