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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

\frac{d}{d x} (\frac{5 x ^{2}}{( x ^{2} + x ) ^{3}})

(- 3, - 1), (2, - 2)

h (x) = \frac{1}{x - 2}, (3, 1)

\int \frac{2 x y}{( x ^{2} + y ^{2} ) ^{2}} d x

\int \frac{4}{x} d x

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