What is the derivative of 6x^5-15x^4+30x^2-30x+9 ?

The derivative of 6x^5-15x^4+30x^2-30x+9 is 30x^4-60x^3+60x-30

What is the first derivative of 6x^5-15x^4+30x^2-30x+9 ?

The first derivative of 6x^5-15x^4+30x^2-30x+9 is 30x^4-60x^3+60x-30

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\frac{d}{d x} (6 x^{5} - 15 x^{4} + 30 x^{2} - 30 x + 9)

30 x^{4} - 60 x^{3} + 60 x - 30

Solution steps

\frac{d}{d x} (6 x^{5} - 15 x^{4} + 30 x^{2} - 30 x + 9)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (6 x^{5}) - \frac{d}{d x} (15 x^{4}) + \frac{d}{d x} (30 x^{2}) - \frac{d}{d x} (30 x) + \frac{d}{d x} (9)

\frac{d}{d x} (6 x^{5}) = 30 x^{4}

\frac{d}{d x} (15 x^{4}) = 60 x^{3}

\frac{d}{d x} (30 x^{2}) = 60 x

\frac{d}{d x} (30 x) = 30

\frac{d}{d x} (9) = 0

= 30 x^{4} - 60 x^{3} + 60 x - 30 + 0

Simplify

= 30 x^{4} - 60 x^{3} + 60 x - 30

What is the derivative of 6x^5-15x^4+30x^2-30x+9 ?
The derivative of 6x^5-15x^4+30x^2-30x+9 is 30x^4-60x^3+60x-30
What is the first derivative of 6x^5-15x^4+30x^2-30x+9 ?
The first derivative of 6x^5-15x^4+30x^2-30x+9 is 30x^4-60x^3+60x-30