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Popular >

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

Solution

derivative of

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

Solution

5 x^{4} - 15 x^{2} + 6

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

2 x (x^{3} - 3 x) + (3 x^{2} - 3) (x^{2} - 2) : 5 x^{4} - 15 x^{2} + 6

= 5 x^{4} - 15 x^{2} + 6

Popular Examples

integral of (tan(3x))/(cos(3x))

\int \frac{tan ( 3 x )}{cos ( 3 x )} d x

5y^{''}+y^'=-10x,y(0)=0,y^'(0)=-15

5 y^{^{''}} + y^{^{'}} = - 10 x, y (0) = 0, y^{^{'}} (0) = - 15

tangent of f(x)=(2x+1)/(x+2),(1,1)tangent of

f (x) = \frac{2 x + 1}{x + 2}, (1, 1)

integral of (x*(sqrt(1-x^4)))

\int (x \cdot (1 - x^{4})) d x

(dy)/(dx)=y^2x^3

\frac{d y}{d x} = y^{2} x^{3}

Frequently Asked Questions (FAQ)

What is the derivative of (x^2-2)(x^3-3x) ?
The derivative of (x^2-2)(x^3-3x) is 5x^4-15x^2+6
What is the first derivative of (x^2-2)(x^3-3x) ?
The first derivative of (x^2-2)(x^3-3x) is 5x^4-15x^2+6