Solve 5y^4*8y^3/4y^2

$$\frac { 5 y ^ { 4 } \times 8 y ^ { 3 } } { 4 y ^ { 2 } }$$

Evaluate

$$10y^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{5y^{7}\times 8}{4y^{2}}$$

Cancel out 4y^{2} in both numerator and denominator.

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

Multiply 2 and 5 to get 10.

$$10y^{5}$$

Differentiate w.r.t. y

$$50y^{4}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{40y^{3}}{4}y^{4-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(10y^{3}y^{2})$$

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}.

$$2\times 10y^{3}y^{2-1}$$

Do the arithmetic.

$$20y^{3}y^{1}$$

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

$$20y^{3}y$$