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

The derivative of (2x^3-3x+1(x^2+5x)) is 10x^4+40x^3-9x^2-28x+5

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

The first derivative of (2x^3-3x+1(x^2+5x)) is 10x^4+40x^3-9x^2-28x+5

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\frac{d}{d x} ((2 x^{3} - 3 x + 1) (x^{2} + 5 x))

10 x^{4} + 40 x^{3} - 9 x^{2} - 28 x + 5

Solution steps

\frac{d}{d x} ((2 x^{3} - 3 x + 1) (x^{2} + 5 x))

Apply the Product Rule:

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

f = 2 x^{3} - 3 x + 1, g = x^{2} + 5 x

= \frac{d}{d x} (2 x^{3} - 3 x + 1) (x^{2} + 5 x) + \frac{d}{d x} (x^{2} + 5 x) (2 x^{3} - 3 x + 1)

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

\frac{d}{d x} (x^{2} + 5 x) = 2 x + 5

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

Simplify

(6 x^{2} - 3) (x^{2} + 5 x) + (2 x + 5) (2 x^{3} - 3 x + 1) : 10 x^{4} + 40 x^{3} - 9 x^{2} - 28 x + 5

= 10 x^{4} + 40 x^{3} - 9 x^{2} - 28 x + 5

i = 1 \sum \infty 3 (\frac{1}{4})^{i - 1}

\int_{0}^{1} e^{x} tan (e^{x}) d x

x \to \infty + lim (3^{- x})

x \to 1 lim (\frac{in ( x )}{x - 1})

y = x^{2} + 10 x

What is the derivative of (2x^3-3x+1(x^2+5x)) ?
The derivative of (2x^3-3x+1(x^2+5x)) is 10x^4+40x^3-9x^2-28x+5
What is the first derivative of (2x^3-3x+1(x^2+5x)) ?
The first derivative of (2x^3-3x+1(x^2+5x)) is 10x^4+40x^3-9x^2-28x+5