Solve 15u^2/35u^5

$$\frac { 15 u ^ { 2 } } { 35 u ^ { 5 } }$$

Evaluate

$$\frac{3}{7u^{3}}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(15u^{2}\right)^{1}\times \frac{1}{35u^{5}}$$

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

$$15^{1}\left(u^{2}\right)^{1}\times \frac{1}{35}\times \frac{1}{u^{5}}$$

Use the Commutative Property of Multiplication.

$$15^{1}\times \frac{1}{35}\left(u^{2}\right)^{1}\times \frac{1}{u^{5}}$$

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

$$15^{1}\times \frac{1}{35}u^{2}u^{5\left(-1\right)}$$

Multiply 5 times -1.

$$15^{1}\times \frac{1}{35}u^{2}u^{-5}$$

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

$$15^{1}\times \frac{1}{35}u^{2-5}$$

Add the exponents 2 and -5.

$$15^{1}\times \frac{1}{35}u^{-3}$$

Raise 15 to the power 1.

$$15\times \frac{1}{35}u^{-3}$$

Multiply 15 times \frac{1}{35}.

$$\frac{3}{7}u^{-3}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{15^{1}u^{2}}{35^{1}u^{5}}$$

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

$$\frac{15^{1}u^{2-5}}{35^{1}}$$

Subtract 5 from 2.

$$\frac{15^{1}u^{-3}}{35^{1}}$$

Reduce the fraction \frac{15}{35} to lowest terms by extracting and canceling out 5.

$$\frac{3}{7}u^{-3}$$

Differentiate w.r.t. u

$$-\frac{9}{7u^{4}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}u}(\frac{15}{35}u^{2-5})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}u}(\frac{3}{7}u^{-3})$$

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}.

$$-3\times \frac{3}{7}u^{-3-1}$$

Do the arithmetic.

$$-\frac{9}{7}u^{-4}$$