Solve (-2x^2sqrt{3})(5xsqrt{6})

$$( - 2 x ^ { 2 } \sqrt { 3 } ) ( 5 x \sqrt { 6 } )$$

Evaluate

$$-30\sqrt{2}x^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$-2x^{3}\sqrt{3}\times 5\sqrt{6}$$

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

$$-2x^{3}\sqrt{3}\times 5\sqrt{3}\sqrt{2}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$-2x^{3}\times 3\times 5\sqrt{2}$$

Multiply -2 and 3 to get -6.

$$-6x^{3}\times 5\sqrt{2}$$

Multiply -6 and 5 to get -30.

$$-30x^{3}\sqrt{2}$$

Differentiate w.r.t. x

$$-90\sqrt{2}x^{2}$$