Solve 80x^4y^2div(5x*8y)

$$80 x ^ { 4 } y ^ { 2 } \div ( 5 x \times 8 y )$$

Differentiate w.r.t. x

$$6yx^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{80y^{2}}{40y}x^{4-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2yx^{3})$$

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}.

$$3\times 2yx^{3-1}$$

Do the arithmetic.

$$6yx^{2}$$

Evaluate

$$2yx^{3}$$

Solution Steps

Cancel out 5\times 8xy in both numerator and denominator.

$$2yx^{3}$$