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Popular >

derivative of (x^3+1(3-2x^3))

Solution

\frac{d}{d x} ((x^{3} + 1) (3 - 2 x^{3}))

Solution

- 12 x^{5} + 3 x^{2}

Solution steps

\frac{d}{d x} ((x^{3} + 1) (3 - 2 x^{3}))

Apply the Product Rule:

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

f = x^{3} + 1, g = 3 - 2 x^{3}

= \frac{d}{d x} (x^{3} + 1) (3 - 2 x^{3}) + \frac{d}{d x} (3 - 2 x^{3}) (x^{3} + 1)

\frac{d}{d x} (x^{3} + 1) = 3 x^{2}

\frac{d}{d x} (3 - 2 x^{3}) = - 6 x^{2}

= 3 x^{2} (3 - 2 x^{3}) + (- 6 x^{2}) (x^{3} + 1)

Simplify

3 x^{2} (3 - 2 x^{3}) + (- 6 x^{2}) (x^{3} + 1) : - 12 x^{5} + 3 x^{2}

= - 12 x^{5} + 3 x^{2}

Popular Examples

slope of (3,2),(5,6)slope

(3, 2), (5, 6)

area y=4x,y= 7/5 x,y=32-x^2 area

y = 4 x, y = \frac{7}{5} x, y = 32 - x^{2}

derivative of (x-5xsqrt(x)/(sqrt(x)))

\frac{d}{d x} (\frac{x - 5 x x}{x})

derivative of xe^x-1

\frac{d}{d x} (x e^{x} - 1)

tangent of f(x)=5x-4x^2,\at x=-1 tangent of

f (x) = 5 x - 4 x^{2}, at x = - 1

Frequently Asked Questions (FAQ)

What is the derivative of (x^3+1(3-2x^3)) ?
The derivative of (x^3+1(3-2x^3)) is -12x^5+3x^2
What is the first derivative of (x^3+1(3-2x^3)) ?
The first derivative of (x^3+1(3-2x^3)) is -12x^5+3x^2