What is the derivative of 2x^6-9x^5+15x^4-10x^3+3x-1 ?

The derivative of 2x^6-9x^5+15x^4-10x^3+3x-1 is 12x^5-45x^4+60x^3-30x^2+3

What is the first derivative of 2x^6-9x^5+15x^4-10x^3+3x-1 ?

The first derivative of 2x^6-9x^5+15x^4-10x^3+3x-1 is 12x^5-45x^4+60x^3-30x^2+3

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\frac{d}{d x} (2 x^{6} - 9 x^{5} + 15 x^{4} - 10 x^{3} + 3 x - 1)

12 x^{5} - 45 x^{4} + 60 x^{3} - 30 x^{2} + 3

Solution steps

\frac{d}{d x} (2 x^{6} - 9 x^{5} + 15 x^{4} - 10 x^{3} + 3 x - 1)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (2 x^{6}) - \frac{d}{d x} (9 x^{5}) + \frac{d}{d x} (15 x^{4}) - \frac{d}{d x} (10 x^{3}) + \frac{d}{d x} (3 x) - \frac{d}{d x} (1)

\frac{d}{d x} (2 x^{6}) = 12 x^{5}

\frac{d}{d x} (9 x^{5}) = 45 x^{4}

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

\frac{d}{d x} (10 x^{3}) = 30 x^{2}

\frac{d}{d x} (3 x) = 3

\frac{d}{d x} (1) = 0

= 12 x^{5} - 45 x^{4} + 60 x^{3} - 30 x^{2} + 3 - 0

Simplify

= 12 x^{5} - 45 x^{4} + 60 x^{3} - 30 x^{2} + 3

\frac{d}{d x} (\frac{x ^{2} + x - 12}{x - 4})

x \to 0 lim (\frac{2 x ^{2} + x}{x})

y = \frac{x ^{2}}{5 - 8 x}

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

x \to 0 lim (x^{3} \cdot sin (\frac{1}{x}))

What is the derivative of 2x^6-9x^5+15x^4-10x^3+3x-1 ?
The derivative of 2x^6-9x^5+15x^4-10x^3+3x-1 is 12x^5-45x^4+60x^3-30x^2+3
What is the first derivative of 2x^6-9x^5+15x^4-10x^3+3x-1 ?
The first derivative of 2x^6-9x^5+15x^4-10x^3+3x-1 is 12x^5-45x^4+60x^3-30x^2+3