Solve 31,293(3)^-1.5(w)^-15/31.293w^-1.5

$$\frac { 31,293 ( 3 ) ^ { - 1.5 } ( w ) ^ { - 15 } } { 31.293 w ^ { - 1.5 } }$$

Differentiate w.r.t. w

$$-\frac{1500\sqrt{3}}{w^{14.5}}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{3477\sqrt{3}}{31.293}w^{-15-\left(-1.5\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{1000\sqrt{3}}{9}w^{-13.5})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$-13.5\times \frac{1000\sqrt{3}}{9}w^{-13.5-1}$$

Do the arithmetic.

$$\left(-1500\sqrt{3}\right)w^{-14.5}$$

Evaluate

$$\frac{1000\sqrt{3}}{9w^{13.5}}$$