What is the derivative of 4(x+4^{3/2}) ?

The derivative of 4(x+4^{3/2}) is 6(x+4)^{1/2}

What is the first derivative of 4(x+4^{3/2}) ?

The first derivative of 4(x+4^{3/2}) is 6(x+4)^{1/2}

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

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (x + 4) = 1

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

Simplify

4 \cdot \frac{3 ( x + 4 ) ^{\frac{1}{2}}}{2} \cdot 1 : 6 (x + 4)^{\frac{1}{2}}

= 6 (x + 4)^{\frac{1}{2}}

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What is the derivative of 4(x+4^{3/2}) ?
The derivative of 4(x+4^{3/2}) is 6(x+4)^{1/2}
What is the first derivative of 4(x+4^{3/2}) ?
The first derivative of 4(x+4^{3/2}) is 6(x+4)^{1/2}