Solve 4d^6/5d

$$\frac { 4 d ^ { 6 } } { 5 d }$$

Evaluate

$$\frac{4d^{5}}{5}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{4^{1}d^{6}}{5^{1}d^{1}}$$

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

$$\frac{4^{1}d^{6-1}}{5^{1}}$$

Subtract 1 from 6.

$$\frac{4^{1}d^{5}}{5^{1}}$$

Divide 4 by 5.

$$\frac{4}{5}d^{5}$$

Differentiate w.r.t. d

$$4d^{4}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{4}{5}d^{6-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{4}{5}d^{5})$$

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}.

$$5\times \frac{4}{5}d^{5-1}$$

Do the arithmetic.

$$4d^{4}$$