Solve y^4*3y^2/y^8

$$\frac { y ^ { 4 } \cdot 3 y ^ { 2 } } { y ^ { 8 } }$$

Evaluate

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

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\frac{y^{6}\times 3}{y^{8}}$$

Cancel out y^{6} in both numerator and denominator.

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

Differentiate w.r.t. y

$$-\frac{6}{y^{3}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{3y^{2}}{1}y^{4-8})$$

Do the arithmetic.

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

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}.

$$-4\times 3y^{2}y^{-4-1}$$

Do the arithmetic.

$$\left(-12y^{2}\right)y^{-5}$$