What is the derivative of 400x^{10}+40x^5+1 ?

The derivative of 400x^{10}+40x^5+1 is 4000x^9+200x^4

What is the first derivative of 400x^{10}+40x^5+1 ?

The first derivative of 400x^{10}+40x^5+1 is 4000x^9+200x^4

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derivative of

400 x^{10} + 40 x^{5} + 1

4000 x^{9} + 200 x^{4}

Solution steps

\frac{d}{d x} (400 x^{10} + 40 x^{5} + 1)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (400 x^{10}) + \frac{d}{d x} (40 x^{5}) + \frac{d}{d x} (1)

\frac{d}{d x} (400 x^{10}) = 4000 x^{9}

\frac{d}{d x} (40 x^{5}) = 200 x^{4}

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

= 4000 x^{9} + 200 x^{4} + 0

Simplify

= 4000 x^{9} + 200 x^{4}

What is the derivative of 400x^{10}+40x^5+1 ?
The derivative of 400x^{10}+40x^5+1 is 4000x^9+200x^4
What is the first derivative of 400x^{10}+40x^5+1 ?
The first derivative of 400x^{10}+40x^5+1 is 4000x^9+200x^4