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Popular >

derivative of f(x)=x^7+x^5+x^3+x+1

Solution

derivative of

f (x) = x^{7} + x^{5} + x^{3} + x + 1

Solution

7 x^{6} + 5 x^{4} + 3 x^{2} + 1

Solution steps

\frac{d}{d x} (x^{7} + x^{5} + x^{3} + x + 1)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{7}) + \frac{d}{d x} (x^{5}) + \frac{d}{d x} (x^{3}) + \frac{d x}{d x} + \frac{d}{d x} (1)

\frac{d}{d x} (x^{7}) = 7 x^{6}

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

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

\frac{d x}{d x} = 1

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

= 7 x^{6} + 5 x^{4} + 3 x^{2} + 1 + 0

Simplify

= 7 x^{6} + 5 x^{4} + 3 x^{2} + 1

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=x^7+x^5+x^3+x+1 ?
The derivative of f(x)=x^7+x^5+x^3+x+1 is 7x^6+5x^4+3x^2+1
What is the first derivative of f(x)=x^7+x^5+x^3+x+1 ?
The first derivative of f(x)=x^7+x^5+x^3+x+1 is 7x^6+5x^4+3x^2+1