Solve d^7/2div3/d^4

$$\frac { d ^ { 7 } } { 2 } \div \frac { 3 } { d ^ { 4 } }$$

Evaluate

$$\frac{d^{11}}{6}$$

Solution Steps

Divide \frac{d^{7}}{2} by \frac{3}{d^{4}} by multiplying \frac{d^{7}}{2} by the reciprocal of \frac{3}{d^{4}}.

$$\frac{d^{7}d^{4}}{2\times 3}$$

To multiply powers of the same base, add their exponents. Add 7 and 4 to get 11.

$$\frac{d^{11}}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$\frac{d^{11}}{6}$$

Differentiate w.r.t. d

$$\frac{11d^{10}}{6}$$

Steps Using Definition of a Derivative

Divide \frac{d^{7}}{2} by \frac{3}{d^{4}} by multiplying \frac{d^{7}}{2} by the reciprocal of \frac{3}{d^{4}}.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{d^{7}d^{4}}{2\times 3})$$

To multiply powers of the same base, add their exponents. Add 7 and 4 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{d^{11}}{2\times 3})$$

Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{d^{11}}{6})$$

The derivative of ax^{n} is nax^{n-1}.

$$11\times \frac{1}{6}d^{11-1}$$

Multiply 11 times \frac{1}{6}.

$$\frac{11}{6}d^{11-1}$$

Subtract 1 from 11.

$$\frac{11}{6}d^{10}$$