Solve 288x^6y^10div(-6xy^4)

$$288 x ^ { 6 } y ^ { 10 } \div ( - 6 x y ^ { 4 } )$$

Evaluate

$$-48x^{5}y^{6}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{288^{1}x^{6}y^{10}}{\left(-6\right)^{1}x^{1}y^{4}}$$

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

$$\frac{288^{1}}{\left(-6\right)^{1}}x^{6-1}y^{10-4}$$

Subtract 1 from 6.

$$\frac{288^{1}}{\left(-6\right)^{1}}x^{5}y^{10-4}$$

Subtract 4 from 10.

$$\frac{288^{1}}{\left(-6\right)^{1}}x^{5}y^{6}$$

Divide 288 by -6.

$$-48x^{5}y^{6}$$

Differentiate w.r.t. x

$$-240x^{4}y^{6}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{288y^{10}}{-6y^{4}}x^{6-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-48y^{6}\right)x^{5})$$

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}.

$$5\left(-48y^{6}\right)x^{5-1}$$

Do the arithmetic.

$$\left(-240y^{6}\right)x^{4}$$