What is the derivative of y=x^3(3-x^2) ?

The derivative of y=x^3(3-x^2) is 9x^2-5x^4

What is the first derivative of y=x^3(3-x^2) ?

The first derivative of y=x^3(3-x^2) is 9x^2-5x^4

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derivative of

y = x^{3} (3 - x^{2})

9 x^{2} - 5 x^{4}

Solution steps

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

Apply the Product Rule:

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

f = x^{3}, g = 3 - x^{2}

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

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

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

= 3 x^{2} (3 - x^{2}) + (- 2 x) x^{3}

Simplify

3 x^{2} (3 - x^{2}) + (- 2 x) x^{3} : 9 x^{2} - 5 x^{4}

= 9 x^{2} - 5 x^{4}

\frac{\partial}{\partial x} (sin (π (4 x - 2 y)))

y = 3 x^{2}, at x = 1

\int (sec^{5} (x)) d x

\int sec (\frac{x}{6}) d x

(- 4, 5), (5, - 22)

What is the derivative of y=x^3(3-x^2) ?
The derivative of y=x^3(3-x^2) is 9x^2-5x^4
What is the first derivative of y=x^3(3-x^2) ?
The first derivative of y=x^3(3-x^2) is 9x^2-5x^4