Solve 2sqrt{3}Xsqrt[3]{1.5}X^6sqrt{12}

$$2 \sqrt { 3 } X \sqrt[ 3 ] { 1.5 } X ^ { 6 } \sqrt { 12 }$$

Evaluate

$$6\sqrt[3]{3}\times 2^{\frac{2}{3}}X^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$2\sqrt{3}X^{7}\sqrt[3]{1.5}\sqrt{12}$$

Factor 12=3\times 4. Rewrite the square root of the product \sqrt{3\times 4} as the product of square roots \sqrt{3}\sqrt{4}.

$$2\sqrt{3}X^{7}\sqrt[3]{1.5}\sqrt{3}\sqrt{4}$$

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

$$2\times 3X^{7}\sqrt[3]{1.5}\sqrt{4}$$

Multiply 2 and 3 to get 6.

$$6X^{7}\sqrt[3]{1.5}\sqrt{4}$$

Calculate the square root of 4 and get 2.

$$6X^{7}\sqrt[3]{1.5}\times 2$$

Multiply 6 and 2 to get 12.

$$12X^{7}\sqrt[3]{1.5}$$

Differentiate w.r.t. X

$$42\sqrt[3]{3}\times 2^{\frac{2}{3}}X^{6}$$