Solve 6a^4b^2c^2/-3a^2{b^2}

$$\frac{ 6 { a }^{ 4 } { b }^{ 2 } { c }^{ 2 } }{ -3 { a }^{ 2 } { b }^{ 2 } }$$

Evaluate

$$-2\left(ac\right)^{2}$$

Solution Steps

Cancel out 3a^{2}b^{2} in both numerator and denominator.

$$\frac{2a^{2}c^{2}}{-1}$$

Anything divided by -1 gives its opposite.

$$-2a^{2}c^{2}$$

Differentiate w.r.t. a

$$-4ac^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{6b^{2}c^{2}}{-3b^{2}}a^{4-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(-2c^{2}\right)a^{2})$$

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}.

$$2\left(-2c^{2}\right)a^{2-1}$$

Do the arithmetic.

$$\left(-4c^{2}\right)a^{1}$$

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

$$\left(-4c^{2}\right)a$$