Solve (6x^{12}y^3z^5):(3x^10y^3z)

$$( 6 x ^ { 12 } y ^ { 3 } z ^ { 5 } ) : ( 3 x ^ { 10 } y ^ { 3 } z )$$

Differentiate w.r.t. x

$$4xz^{4}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6y^{3}z^{5}}{3zy^{3}}x^{12-10})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$4z^{4}x^{1}$$

For any term t, t^{1}=t.

$$4z^{4}x$$

Evaluate

$$2x^{2}z^{4}$$

Solution Steps

Cancel out 3zy^{3}x^{10} in both numerator and denominator.

$$2x^{2}z^{4}$$