Solve 2vx^{2}*3x^2v^-2*7u^5u^-8

$$2 v x ^ { 2 } \cdot 3 x ^ { 2 } v ^ { - 2 } \cdot 7 u ^ { 5 } u ^ { - 8 }$$

Evaluate

$$\frac{42x^{4}}{vu^{3}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and -2 to get -1.

$$2v^{-1}x^{2}\times 3x^{2}\times 7u^{5}u^{-8}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$2v^{-1}x^{4}\times 3\times 7u^{5}u^{-8}$$

To multiply powers of the same base, add their exponents. Add 5 and -8 to get -3.

$$2v^{-1}x^{4}\times 3\times 7u^{-3}$$

Multiply 2 and 3 to get 6.

$$6v^{-1}x^{4}\times 7u^{-3}$$

Multiply 6 and 7 to get 42.

$$42v^{-1}x^{4}u^{-3}$$

Differentiate w.r.t. x

$$\frac{168\times \left(\frac{x}{u}\right)^{3}}{v}$$