What is the derivative of 8(x+4^{3/2}) ?

The derivative of 8(x+4^{3/2}) is 12(x+4)^{1/2}

What is the first derivative of 8(x+4^{3/2}) ?

The first derivative of 8(x+4^{3/2}) is 12(x+4)^{1/2}

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\frac{d}{d x} (8 (x + 4)^{\frac{3}{2}})

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

Solution steps

\frac{d}{d x} (8 (x + 4)^{\frac{3}{2}})

Take the constant out:

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

= 8 \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

= 8 \cdot \frac{3 ( x + 4 ) ^{\frac{1}{2}}}{2} \cdot 1

Simplify

8 \cdot \frac{3 ( x + 4 ) ^{\frac{1}{2}}}{2} \cdot 1 : 12 (x + 4)^{\frac{1}{2}}

= 12 (x + 4)^{\frac{1}{2}}

What is the derivative of 8(x+4^{3/2}) ?
The derivative of 8(x+4^{3/2}) is 12(x+4)^{1/2}
What is the first derivative of 8(x+4^{3/2}) ?
The first derivative of 8(x+4^{3/2}) is 12(x+4)^{1/2}