Solve 30u/5u^5

$$\frac { 30 u } { 5 u ^ { 5 } }$$

Evaluate

$$\frac{6}{u^{4}}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(30u^{1}\right)^{1}\times \frac{1}{5u^{5}}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$30^{1}\left(u^{1}\right)^{1}\times \frac{1}{5}\times \frac{1}{u^{5}}$$

Use the Commutative Property of Multiplication.

$$30^{1}\times \frac{1}{5}\left(u^{1}\right)^{1}\times \frac{1}{u^{5}}$$

To raise a power to another power, multiply the exponents.

$$30^{1}\times \frac{1}{5}u^{1}u^{5\left(-1\right)}$$

Multiply 5 times -1.

$$30^{1}\times \frac{1}{5}u^{1}u^{-5}$$

To multiply powers of the same base, add their exponents.

$$30^{1}\times \frac{1}{5}u^{1-5}$$

Add the exponents 1 and -5.

$$30^{1}\times \frac{1}{5}u^{-4}$$

Raise 30 to the power 1.

$$30\times \frac{1}{5}u^{-4}$$

Multiply 30 times \frac{1}{5}.

$$6u^{-4}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{30^{1}u^{1}}{5^{1}u^{5}}$$

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

$$\frac{30^{1}u^{1-5}}{5^{1}}$$

Subtract 5 from 1.

$$\frac{30^{1}u^{-4}}{5^{1}}$$

Divide 30 by 5.

$$6u^{-4}$$

Differentiate w.r.t. u

$$-\frac{24}{u^{5}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}u}(\frac{30}{5}u^{1-5})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}u}(6u^{-4})$$

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}.

$$-4\times 6u^{-4-1}$$

Do the arithmetic.

$$-24u^{-5}$$