What is the derivative of (x^2+17(x^3-3x+1)) ?

The derivative of (x^2+17(x^3-3x+1)) is 5x^4+42x^2+2x-51

What is the first derivative of (x^2+17(x^3-3x+1)) ?

The first derivative of (x^2+17(x^3-3x+1)) is 5x^4+42x^2+2x-51

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\frac{d}{d x} ((x^{2} + 17) (x^{3} - 3 x + 1))

5 x^{4} + 42 x^{2} + 2 x - 51

Solution steps

\frac{d}{d x} ((x^{2} + 17) (x^{3} - 3 x + 1))

Apply the Product Rule:

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

f = x^{2} + 17, g = x^{3} - 3 x + 1

= \frac{d}{d x} (x^{2} + 17) (x^{3} - 3 x + 1) + \frac{d}{d x} (x^{3} - 3 x + 1) (x^{2} + 17)

\frac{d}{d x} (x^{2} + 17) = 2 x

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

= 2 x (x^{3} - 3 x + 1) + (3 x^{2} - 3) (x^{2} + 17)

Simplify

2 x (x^{3} - 3 x + 1) + (3 x^{2} - 3) (x^{2} + 17) : 5 x^{4} + 42 x^{2} + 2 x - 51

= 5 x^{4} + 42 x^{2} + 2 x - 51

y^{^{''}} + 9 y = 9 x^{2} + 9 x + 11

x \frac{d y}{d x} + y ln (x) - y = y ln (y)

\frac{\partial}{\partial y} (\frac{1}{x ^{2} yz})

\frac{d y}{d t} - \frac{5}{t} y = t^{5}

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

What is the derivative of (x^2+17(x^3-3x+1)) ?
The derivative of (x^2+17(x^3-3x+1)) is 5x^4+42x^2+2x-51
What is the first derivative of (x^2+17(x^3-3x+1)) ?
The first derivative of (x^2+17(x^3-3x+1)) is 5x^4+42x^2+2x-51