Solve 45x^4/5x

$$\frac { 45 x ^ { 4 } } { 5 x }$$

Evaluate

$$9x^{3}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{45^{1}x^{4}}{5^{1}x^{1}}$$

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

$$\frac{45^{1}x^{4-1}}{5^{1}}$$

Subtract 1 from 4.

$$\frac{45^{1}x^{3}}{5^{1}}$$

Divide 45 by 5.

$$9x^{3}$$

Differentiate w.r.t. x

$$27x^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{45}{5}x^{4-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x^{3})$$

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}.

$$3\times 9x^{3-1}$$

Do the arithmetic.

$$27x^{2}$$