Solve (-6xy)(10x^5y^2)/-4x^6y

$$\frac { ( - 6 x y ) ( 10 x ^ { 5 } y ^ { 2 } ) } { - 4 x ^ { 6 } y }$$

Evaluate

$$15y^{2}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

$$\frac{-6x^{6}y\times 10y^{2}}{-4x^{6}y}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{-6x^{6}y^{3}\times 10}{-4x^{6}y}$$

Cancel out 2\times 2yx^{6} in both numerator and denominator.

$$\frac{-3\times 5y^{2}}{-1}$$

Multiply -3 and 5 to get -15.

$$\frac{-15y^{2}}{-1}$$

Anything divided by -1 gives its opposite.

$$15y^{2}$$

Differentiate w.r.t. y

$$30y$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{-6x^{6}y\times 10y^{2}}{-4x^{6}y})$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{-6x^{6}y^{3}\times 10}{-4x^{6}y})$$

Cancel out 2\times 2yx^{6} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{-3\times 5y^{2}}{-1})$$

Multiply -3 and 5 to get -15.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{-15y^{2}}{-1})$$

Anything divided by -1 gives its opposite.

$$\frac{\mathrm{d}}{\mathrm{d}y}(15y^{2})$$

The derivative of ax^{n} is nax^{n-1}.

$$2\times 15y^{2-1}$$

Multiply 2 times 15.

$$30y^{2-1}$$

Subtract 1 from 2.

$$30y^{1}$$

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

$$30y$$