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

The derivative of 2x^6+3x^5+4x^4-5x^3-6x^2+1 is 12x^5+15x^4+16x^3-15x^2-12x

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

The first derivative of 2x^6+3x^5+4x^4-5x^3-6x^2+1 is 12x^5+15x^4+16x^3-15x^2-12x

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

12 x^{5} + 15 x^{4} + 16 x^{3} - 15 x^{2} - 12 x

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (3 x^{5}) = 15 x^{4}

\frac{d}{d x} (4 x^{4}) = 16 x^{3}

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

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

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

= 12 x^{5} + 15 x^{4} + 16 x^{3} - 15 x^{2} - 12 x + 0

Simplify

= 12 x^{5} + 15 x^{4} + 16 x^{3} - 15 x^{2} - 12 x

ln (x^{2} + 1)

- 6 t (5 t^{3} - 1)^{7}

x \to - 3 lim (x^{2} - 5)

x \to 2 - lim (\frac{2 x}{x - 2})

x \to c + lim (g (x))

What is the derivative of 2x^6+3x^5+4x^4-5x^3-6x^2+1 ?
The derivative of 2x^6+3x^5+4x^4-5x^3-6x^2+1 is 12x^5+15x^4+16x^3-15x^2-12x
What is the first derivative of 2x^6+3x^5+4x^4-5x^3-6x^2+1 ?
The first derivative of 2x^6+3x^5+4x^4-5x^3-6x^2+1 is 12x^5+15x^4+16x^3-15x^2-12x