Solve 3v^{8}v^-8u^-4u*2x^9*7x^6

$$3 v ^ { 8 } v ^ { - 8 } u ^ { - 4 } u \cdot 2 x ^ { 9 } \cdot 7 x ^ { 6 }$$

Evaluate

$$\frac{42x^{15}}{u^{3}}$$

Solution Steps

Multiply v^{8} and v^{-8} to get 1.

$$3u^{-4}u\times 2x^{9}\times 7x^{6}$$

To multiply powers of the same base, add their exponents. Add -4 and 1 to get -3.

$$3u^{-3}\times 2x^{9}\times 7x^{6}$$

To multiply powers of the same base, add their exponents. Add 9 and 6 to get 15.

$$3u^{-3}\times 2x^{15}\times 7$$

Multiply 3 and 2 to get 6.

$$6u^{-3}x^{15}\times 7$$

Multiply 6 and 7 to get 42.

$$42u^{-3}x^{15}$$

Differentiate w.r.t. x

$$\frac{630x^{14}}{u^{3}}$$