What is the derivative of 4+2x-3x^2-5x^3-8x^4+9x^5 ?

The derivative of 4+2x-3x^2-5x^3-8x^4+9x^5 is 45x^4-32x^3-15x^2-6x+2

What is the first derivative of 4+2x-3x^2-5x^3-8x^4+9x^5 ?

The first derivative of 4+2x-3x^2-5x^3-8x^4+9x^5 is 45x^4-32x^3-15x^2-6x+2

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\frac{d}{d x} (4 + 2 x - 3 x^{2} - 5 x^{3} - 8 x^{4} + 9 x^{5})

45 x^{4} - 32 x^{3} - 15 x^{2} - 6 x + 2

Solution steps

\frac{d}{d x} (4 + 2 x - 3 x^{2} - 5 x^{3} - 8 x^{4} + 9 x^{5})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (4) + \frac{d}{d x} (2 x) - \frac{d}{d x} (3 x^{2}) - \frac{d}{d x} (5 x^{3}) - \frac{d}{d x} (8 x^{4}) + \frac{d}{d x} (9 x^{5})

\frac{d}{d x} (4) = 0

\frac{d}{d x} (2 x) = 2

\frac{d}{d x} (3 x^{2}) = 6 x

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

\frac{d}{d x} (8 x^{4}) = 32 x^{3}

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

= 0 + 2 - 6 x - 15 x^{2} - 32 x^{3} + 45 x^{4}

Simplify

= 45 x^{4} - 32 x^{3} - 15 x^{2} - 6 x + 2

What is the derivative of 4+2x-3x^2-5x^3-8x^4+9x^5 ?
The derivative of 4+2x-3x^2-5x^3-8x^4+9x^5 is 45x^4-32x^3-15x^2-6x+2
What is the first derivative of 4+2x-3x^2-5x^3-8x^4+9x^5 ?
The first derivative of 4+2x-3x^2-5x^3-8x^4+9x^5 is 45x^4-32x^3-15x^2-6x+2