What is the derivative of 17.5(x+1^{0.75}) ?

The derivative of 17.5(x+1^{0.75}) is (13.125)/((x+1)^{0.25)}

What is the first derivative of 17.5(x+1^{0.75}) ?

The first derivative of 17.5(x+1^{0.75}) is (13.125)/((x+1)^{0.25)}

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\frac{d}{d x} (17.5 (x + 1)^{0.75})

\frac{13.125}{( x + 1 ) ^{0.25}}

Solution steps

\frac{d}{d x} (17.5 (x + 1)^{0.75})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 17.5 \frac{d}{d x} ((x + 1)^{0.75})

Apply the chain rule:

\frac{0.75}{( x + 1 ) ^{0.25}} \frac{d}{d x} (x + 1)

= \frac{0.75}{( x + 1 ) ^{0.25}} \frac{d}{d x} (x + 1)

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

= 17.5 \cdot \frac{0.75}{( x + 1 ) ^{0.25}} \cdot 1

Simplify

17.5 \cdot \frac{0.75}{( x + 1 ) ^{0.25}} \cdot 1 : \frac{13.125}{( x + 1 ) ^{0.25}}

= \frac{13.125}{( x + 1 ) ^{0.25}}

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\frac{8 x}{( x ^{2} + 1 )}

x \to 0 - lim (ln (x))

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What is the derivative of 17.5(x+1^{0.75}) ?
The derivative of 17.5(x+1^{0.75}) is (13.125)/((x+1)^{0.25)}
What is the first derivative of 17.5(x+1^{0.75}) ?
The first derivative of 17.5(x+1^{0.75}) is (13.125)/((x+1)^{0.25)}