What is the derivative of 8x^5+45x^4+80x^3+50x^2+200 ?

The derivative of 8x^5+45x^4+80x^3+50x^2+200 is 40x^4+180x^3+240x^2+100x

What is the first derivative of 8x^5+45x^4+80x^3+50x^2+200 ?

The first derivative of 8x^5+45x^4+80x^3+50x^2+200 is 40x^4+180x^3+240x^2+100x

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\frac{d}{d x} (8 x^{5} + 45 x^{4} + 80 x^{3} + 50 x^{2} + 200)

40 x^{4} + 180 x^{3} + 240 x^{2} + 100 x

Solution steps

\frac{d}{d x} (8 x^{5} + 45 x^{4} + 80 x^{3} + 50 x^{2} + 200)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (8 x^{5}) + \frac{d}{d x} (45 x^{4}) + \frac{d}{d x} (80 x^{3}) + \frac{d}{d x} (50 x^{2}) + \frac{d}{d x} (200)

\frac{d}{d x} (8 x^{5}) = 40 x^{4}

\frac{d}{d x} (45 x^{4}) = 180 x^{3}

\frac{d}{d x} (80 x^{3}) = 240 x^{2}

\frac{d}{d x} (50 x^{2}) = 100 x

\frac{d}{d x} (200) = 0

= 40 x^{4} + 180 x^{3} + 240 x^{2} + 100 x + 0

Simplify

= 40 x^{4} + 180 x^{3} + 240 x^{2} + 100 x

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What is the derivative of 8x^5+45x^4+80x^3+50x^2+200 ?
The derivative of 8x^5+45x^4+80x^3+50x^2+200 is 40x^4+180x^3+240x^2+100x
What is the first derivative of 8x^5+45x^4+80x^3+50x^2+200 ?
The first derivative of 8x^5+45x^4+80x^3+50x^2+200 is 40x^4+180x^3+240x^2+100x