Solve 16w^9y^-2z^-6/4w^6{y^-2{z}^-12}

$$\frac{ 16 { w }^{ 9 } { y }^{ -2 } { z }^{ -6 } }{ 4 { w }^{ 6 } { y }^{ -2 } { z }^{ -12 } }$$

Evaluate

$$4w^{3}z^{6}$$

Solution Steps

Cancel out 4y^{-2}w^{6} in both numerator and denominator.

$$\frac{4z^{-6}w^{3}}{z^{-12}}$$

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

$$4w^{3}z^{6}$$

Differentiate w.r.t. w

$$12w^{2}z^{6}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{16}{y^{2}z^{6}\times \frac{4}{y^{2}z^{12}}}w^{9-6})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}w}(4z^{6}w^{3})$$

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}.

$$3\times 4z^{6}w^{3-1}$$

Do the arithmetic.

$$12z^{6}w^{2}$$