Solve 9c/4c^2

$$\frac { 9 c } { 4 c ^ { 2 } }$$

Evaluate

$$\frac{9}{4c}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(9c^{1}\right)^{1}\times \frac{1}{4c^{2}}$$

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

$$9^{1}\left(c^{1}\right)^{1}\times \frac{1}{4}\times \frac{1}{c^{2}}$$

Use the Commutative Property of Multiplication.

$$9^{1}\times \frac{1}{4}\left(c^{1}\right)^{1}\times \frac{1}{c^{2}}$$

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

$$9^{1}\times \frac{1}{4}c^{1}c^{2\left(-1\right)}$$

Multiply 2 times -1.

$$9^{1}\times \frac{1}{4}c^{1}c^{-2}$$

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

$$9^{1}\times \frac{1}{4}c^{1-2}$$

Add the exponents 1 and -2.

$$9^{1}\times \frac{1}{4}\times \frac{1}{c}$$

Raise 9 to the power 1.

$$9\times \frac{1}{4}\times \frac{1}{c}$$

Multiply 9 times \frac{1}{4}.

$$\frac{9}{4}\times \frac{1}{c}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{9^{1}c^{1}}{4^{1}c^{2}}$$

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

$$\frac{9^{1}c^{1-2}}{4^{1}}$$

Subtract 2 from 1.

$$\frac{9^{1}\times \frac{1}{c}}{4^{1}}$$

Divide 9 by 4.

$$\frac{9}{4}\times \frac{1}{c}$$

Differentiate w.r.t. c

$$-\frac{9}{4c^{2}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{9}{4}c^{1-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{9}{4}\times \frac{1}{c})$$

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}.

$$-\frac{9}{4}c^{-1-1}$$

Do the arithmetic.

$$-\frac{9}{4}c^{-2}$$