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Popular >

derivative of y=x^3(9-x^2)

Solution

derivative of

y = x^{3} (9 - x^{2})

Solution

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

Solution steps

\frac{d}{d x} (x^{3} (9 - x^{2}))

Apply the Product Rule:

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

f = x^{3}, g = 9 - x^{2}

= \frac{d}{d x} (x^{3}) (9 - x^{2}) + \frac{d}{d x} (9 - x^{2}) x^{3}

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

\frac{d}{d x} (9 - x^{2}) = - 2 x

= 3 x^{2} (9 - x^{2}) + (- 2 x) x^{3}

Simplify

3 x^{2} (9 - x^{2}) + (- 2 x) x^{3} : 27 x^{2} - 5 x^{4}

= 27 x^{2} - 5 x^{4}

Popular Examples

derivative of 2x^7+3x+11 derivative of

2 x^{7} + 3 x + 11

(\partial)/(\partial x)(x/(2*sqrt(2)))

\frac{\partial}{\partial x} (\frac{x}{2 \cdot 2})

1+y^2+2(t+1)y(dy)/(dt)=0,y(0)=1

1 + y^{2} + 2 (t + 1) y \frac{d y}{d t} = 0, y (0) = 1

x(dy)/(dx)+(1-3x)y=e^{5x}

x \frac{d y}{d x} + (1 - 3 x) y = e^{5 x}

f(x)=(sin(x))/(e^x)

f (x) = \frac{sin ( x )}{e ^{x}}

Frequently Asked Questions (FAQ)

What is the derivative of y=x^3(9-x^2) ?
The derivative of y=x^3(9-x^2) is 27x^2-5x^4
What is the first derivative of y=x^3(9-x^2) ?
The first derivative of y=x^3(9-x^2) is 27x^2-5x^4