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

The derivative of (5x^3+3(x^4-2x)) is 35x^6-28x^3-6

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

The first derivative of (5x^3+3(x^4-2x)) is 35x^6-28x^3-6

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\frac{d}{d x} ((5 x^{3} + 3) (x^{4} - 2 x))

35 x^{6} - 28 x^{3} - 6

Solution steps

\frac{d}{d x} ((5 x^{3} + 3) (x^{4} - 2 x))

Apply the Product Rule:

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

f = 5 x^{3} + 3, g = x^{4} - 2 x

= \frac{d}{d x} (5 x^{3} + 3) (x^{4} - 2 x) + \frac{d}{d x} (x^{4} - 2 x) (5 x^{3} + 3)

\frac{d}{d x} (5 x^{3} + 3) = 15 x^{2}

\frac{d}{d x} (x^{4} - 2 x) = 4 x^{3} - 2

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

Simplify

15 x^{2} (x^{4} - 2 x) + (4 x^{3} - 2) (5 x^{3} + 3) : 35 x^{6} - 28 x^{3} - 6

= 35 x^{6} - 28 x^{3} - 6

t e^{2 t} sin (t)

\frac{d y}{d x} + 2 y = e^{- x}

X^{3} - X^{2} + 4 X + 5

f (x) = \frac{125}{x ^{2} + 24}, at x = - 1

What is the derivative of (5x^3+3(x^4-2x)) ?
The derivative of (5x^3+3(x^4-2x)) is 35x^6-28x^3-6
What is the first derivative of (5x^3+3(x^4-2x)) ?
The first derivative of (5x^3+3(x^4-2x)) is 35x^6-28x^3-6