Solve frac{8v^{9}(-4)^{4}w^9}{4v^3(-4)^2w^8}

$$\frac { 8 v ^ { 9 } ( - 4 ) ^ { 4 } w ^ { 9 } } { 4 v ^ { 3 } ( - 4 ) ^ { 2 } w ^ { 8 } }$$

Evaluate

$$32wv^{6}$$

Solution Steps

Cancel out 4\left(-4\right)^{2}v^{3}w^{8} in both numerator and denominator.

$$2\left(-4\right)^{2}wv^{6}$$

Calculate -4 to the power of 2 and get 16.

$$2\times 16wv^{6}$$

Multiply 2 and 16 to get 32.

$$32wv^{6}$$

Differentiate w.r.t. v

$$192wv^{5}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{2048w^{9}}{64w^{8}}v^{9-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}v}(32wv^{6})$$

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}.

$$6\times 32wv^{6-1}$$

Do the arithmetic.

$$192wv^{5}$$