What is the derivative of (1+x^n) ?

The derivative of (1+x^n) is n(1+x)^{n-1}

What is the first derivative of (1+x^n) ?

The first derivative of (1+x^n) is n(1+x)^{n-1}

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\frac{d}{d x} ((1 + x)^{n})

n (1 + x)^{n - 1}

Solution steps

\frac{d}{d x} ((1 + x)^{n})

Apply the chain rule:

n (1 + x)^{n - 1} \frac{d}{d x} (1 + x)

= n (1 + x)^{n - 1} \frac{d}{d x} (1 + x)

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

= n (1 + x)^{n - 1} \cdot 1

Simplify

= n (1 + x)^{n - 1}

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\frac{d}{d x} (\frac{1 + csc ( x )}{1 + sec ( x )})

(1 + 4 x)^{\frac{3}{2}}

\frac{d}{d x} (\frac{11 x}{2 + x ^{2}})

What is the derivative of (1+x^n) ?
The derivative of (1+x^n) is n(1+x)^{n-1}
What is the first derivative of (1+x^n) ?
The first derivative of (1+x^n) is n(1+x)^{n-1}