Solve -3y/-4y^2

$$\frac { - 3 y } { - 4 y ^ { 2 } }$$

Evaluate

$$\frac{3}{4y}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(-3y^{1}\right)^{1}\times \frac{1}{-4y^{2}}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$\left(-3\right)^{1}\left(y^{1}\right)^{1}\times \frac{1}{-4}\times \frac{1}{y^{2}}$$

Use the Commutative Property of Multiplication.

$$\left(-3\right)^{1}\times \frac{1}{-4}\left(y^{1}\right)^{1}\times \frac{1}{y^{2}}$$

To raise a power to another power, multiply the exponents.

$$\left(-3\right)^{1}\times \frac{1}{-4}y^{1}y^{2\left(-1\right)}$$

Multiply 2 times -1.

$$\left(-3\right)^{1}\times \frac{1}{-4}y^{1}y^{-2}$$

To multiply powers of the same base, add their exponents.

$$\left(-3\right)^{1}\times \frac{1}{-4}y^{1-2}$$

Add the exponents 1 and -2.

$$\left(-3\right)^{1}\times \frac{1}{-4}\times \frac{1}{y}$$

Raise -3 to the power 1.

$$-3\times \frac{1}{-4}\times \frac{1}{y}$$

Raise -4 to the power -1.

$$-3\left(-\frac{1}{4}\right)\times \frac{1}{y}$$

Multiply -3 times -\frac{1}{4}.

$$\frac{3}{4}\times \frac{1}{y}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{\left(-3\right)^{1}y^{1}}{\left(-4\right)^{1}y^{2}}$$

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

$$\frac{\left(-3\right)^{1}y^{1-2}}{\left(-4\right)^{1}}$$

Subtract 2 from 1.

$$\frac{\left(-3\right)^{1}\times \frac{1}{y}}{\left(-4\right)^{1}}$$

Divide -3 by -4.

$$\frac{3}{4}\times \frac{1}{y}$$

Differentiate w.r.t. y

$$-\frac{3}{4y^{2}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\left(-\frac{3}{-4}\right)y^{1-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{3}{4}\times \frac{1}{y})$$

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}.

$$-\frac{3}{4}y^{-1-1}$$

Do the arithmetic.

$$-\frac{3}{4}y^{-2}$$