Solve frac{(-6x^{3}y^{3})*(-7x^4y^2)}{14x^5y^5}

$$\frac { ( - 6 x ^ { 3 } y ^ { 3 } ) \times ( - 7 x ^ { 4 } y ^ { 2 } ) } { 14 x ^ { 5 } y ^ { 5 } }$$

Evaluate

$$3x^{2}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{-6x^{7}y^{3}\left(-7\right)y^{2}}{14x^{5}y^{5}}$$

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

$$\frac{-6x^{7}y^{5}\left(-7\right)}{14x^{5}y^{5}}$$

Cancel out 2\times 7x^{5}y^{5} in both numerator and denominator.

$$-3\left(-1\right)x^{2}$$

Multiply -3 and -1 to get 3.

$$3x^{2}$$

Differentiate w.r.t. x

$$6x$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{42x^{4}y^{5}}{14y^{5}}x^{3-5})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{4}x^{-2})$$

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}.

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

Do the arithmetic.

$$\left(-6x^{4}\right)x^{-3}$$