What is the derivative of 12x^5+45x^4-200x^3+4 ?

The derivative of 12x^5+45x^4-200x^3+4 is 60x^4+180x^3-600x^2

What is the first derivative of 12x^5+45x^4-200x^3+4 ?

The first derivative of 12x^5+45x^4-200x^3+4 is 60x^4+180x^3-600x^2

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\frac{d}{d x} (12 x^{5} + 45 x^{4} - 200 x^{3} + 4)

60 x^{4} + 180 x^{3} - 600 x^{2}

Solution steps

\frac{d}{d x} (12 x^{5} + 45 x^{4} - 200 x^{3} + 4)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (12 x^{5}) + \frac{d}{d x} (45 x^{4}) - \frac{d}{d x} (200 x^{3}) + \frac{d}{d x} (4)

\frac{d}{d x} (12 x^{5}) = 60 x^{4}

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

\frac{d}{d x} (200 x^{3}) = 600 x^{2}

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

= 60 x^{4} + 180 x^{3} - 600 x^{2} + 0

Simplify

= 60 x^{4} + 180 x^{3} - 600 x^{2}

What is the derivative of 12x^5+45x^4-200x^3+4 ?
The derivative of 12x^5+45x^4-200x^3+4 is 60x^4+180x^3-600x^2
What is the first derivative of 12x^5+45x^4-200x^3+4 ?
The first derivative of 12x^5+45x^4-200x^3+4 is 60x^4+180x^3-600x^2