Solve -5u^5*6u^5v^2/-3uv^2

$$\frac { - 5 u ^ { 5 } \cdot 6 u ^ { 5 } v ^ { 2 } } { - 3 u v ^ { 2 } }$$

Evaluate

$$10u^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 5 to get 10.

$$\frac{-5u^{10}\times 6v^{2}}{-3uv^{2}}$$

Cancel out 3uv^{2} in both numerator and denominator.

$$\frac{-5\times 2u^{9}}{-1}$$

Multiply -5 and 2 to get -10.

$$\frac{-10u^{9}}{-1}$$

Anything divided by -1 gives its opposite.

$$10u^{9}$$

Differentiate w.r.t. u

$$90u^{8}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}u}(\left(-\frac{30v^{2}u^{5}}{-3v^{2}}\right)u^{5-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}u}(10u^{5}u^{4})$$

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}.

$$4\times 10u^{5}u^{4-1}$$

Do the arithmetic.

$$40u^{5}u^{3}$$