What is the derivative of (x^2+3x)(x^3-9x) ?

The derivative of (x^2+3x)(x^3-9x) is 5x^4+12x^3-27x^2-54x

What is the first derivative of (x^2+3x)(x^3-9x) ?

The first derivative of (x^2+3x)(x^3-9x) is 5x^4+12x^3-27x^2-54x

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derivative of

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

5 x^{4} + 12 x^{3} - 27 x^{2} - 54 x

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

(2 x + 3) (x^{3} - 9 x) + (3 x^{2} - 9) (x^{2} + 3 x) : 5 x^{4} + 12 x^{3} - 27 x^{2} - 54 x

= 5 x^{4} + 12 x^{3} - 27 x^{2} - 54 x

x^{2 \cdot x}

6 x^{- 2}

\frac{d}{d x} (sin^{3} (3 x^{7} - 2 x + i))

\frac{2 x}{( x ^{2} + 1 )}

y = (x^{4} + 5 x^{2})^{7}

What is the derivative of (x^2+3x)(x^3-9x) ?
The derivative of (x^2+3x)(x^3-9x) is 5x^4+12x^3-27x^2-54x
What is the first derivative of (x^2+3x)(x^3-9x) ?
The first derivative of (x^2+3x)(x^3-9x) is 5x^4+12x^3-27x^2-54x