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

The derivative of (1+x^y) is (ln(1+x)(dy)/(dx)+y/(1+x))(1+x)^y

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

The first derivative of (1+x^y) is (ln(1+x)(dy)/(dx)+y/(1+x))(1+x)^y

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

(ln (1 + x) \frac{d y}{d x} + \frac{y}{1 + x}) (1 + x)^{y}

Solution steps

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

Apply exponent rule:

a^{b} = e^{b l n (a)}

(1 + x)^{y} = e^{y l n (1 + x)}

= \frac{d}{d x} (e^{y l n (1 + x)})

Apply the chain rule:

e^{y l n (1 + x)} \frac{d}{d x} (y ln (1 + x))

= e^{y l n (1 + x)} \frac{d}{d x} (y ln (1 + x))

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

= e^{y l n (1 + x)} (ln (1 + x) \frac{d y}{d x} + \frac{y}{1 + x})

e^{y l n (1 + x)} = (1 + x)^{y}

= (ln (1 + x) \frac{d y}{d x} + \frac{y}{1 + x}) (1 + x)^{y}

0.8 \cdot 5.67 \cdot 1 0^{- 8} (87 3^{4} - 87 2^{4})

(70) (9.8) (3) \frac{1}{2} (70)^{2}

- 0.070539609 e^{- 57 \cdot 3}

0.24 \cdot 1 0^{- 4}

0.24 \cdot 1 0^{- 3}

What is the derivative of (1+x^y) ?
The derivative of (1+x^y) is (ln(1+x)(dy)/(dx)+y/(1+x))(1+x)^y
What is the first derivative of (1+x^y) ?
The first derivative of (1+x^y) is (ln(1+x)(dy)/(dx)+y/(1+x))(1+x)^y