Solve 2x^2*6x^3/2x^-2

$$\frac{ 2 { x }^{ 2 } \times 6 { x }^{ 3 } }{ 2 { x }^{ -2 } }$$

Evaluate

$$6x^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{2x^{5}\times 6}{2x^{-2}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{6x^{5}}{x^{-2}}$$

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

$$6x^{7}$$

Differentiate w.r.t. x

$$42x^{6}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{12x^{3}}{2}x^{2-\left(-2\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{3}x^{4})$$

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}.

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

Do the arithmetic.

$$24x^{3}x^{3}$$