Solve 20h/h^3

$$\frac { 20 h } { h ^ { 3 } }$$

Evaluate

$$\frac{20}{h^{2}}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(20h^{1}\right)^{1}\times \frac{1}{h^{3}}$$

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

$$20^{1}\left(h^{1}\right)^{1}\times \frac{1}{1}\times \frac{1}{h^{3}}$$

Use the Commutative Property of Multiplication.

$$20^{1}\times \frac{1}{1}\left(h^{1}\right)^{1}\times \frac{1}{h^{3}}$$

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

$$20^{1}\times \frac{1}{1}h^{1}h^{3\left(-1\right)}$$

Multiply 3 times -1.

$$20^{1}\times \frac{1}{1}h^{1}h^{-3}$$

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

$$20^{1}\times \frac{1}{1}h^{1-3}$$

Add the exponents 1 and -3.

$$20^{1}\times \frac{1}{1}h^{-2}$$

Raise 20 to the power 1.

$$20\times \frac{1}{1}h^{-2}$$

Differentiate w.r.t. h

$$-\frac{40}{h^{3}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{20}{1}h^{1-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}h}(20h^{-2})$$

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}.

$$-2\times 20h^{-2-1}$$

Do the arithmetic.

$$-40h^{-3}$$