Solve 5*2y/2*y^4

$$\frac { 5 \times 2 y } { 2 \times y ^ { 4 } }$$

Differentiate w.r.t. y

$$-\frac{15}{y^{4}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{10}{2}y^{1-4})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$-15y^{-4}$$

Evaluate

$$\frac{5}{y^{3}}$$

Solution Steps

Cancel out 2y in both numerator and denominator.

$$\frac{5}{y^{3}}$$