Solve frac{8w^{8}(2)^3x^2}{4w^2(2)x^2}

$$\frac { 8 w ^ { 8 } ( 2 ) ^ { 3 } x ^ { 2 } } { 4 w ^ { 2 } ( 2 ) x ^ { 2 } }$$

Evaluate

$$8w^{6}$$

Solution Steps

Cancel out 2\times 4w^{2}x^{2} in both numerator and denominator.

$$2^{3}w^{6}$$

Calculate 2 to the power of 3 and get 8.

$$8w^{6}$$

Differentiate w.r.t. w

$$48w^{5}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{64x^{2}}{8x^{2}}w^{8-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}w}(8w^{6})$$

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}.

$$6\times 8w^{6-1}$$

Do the arithmetic.

$$48w^{5}$$