Solve 7!*c_9^2/9^7=

$$\frac { 7 ! \cdot c _ { 9 } ^ { 2 } } { 9 ^ { 7 } } =$$

Evaluate

$$5040c_{9}^{2}$$

Solution Steps

Cancel out 9^{7} in both numerator and denominator.

$$7!c_{9}^{2}$$

The factorial of 7 is 5040.

$$5040c_{9}^{2}$$

Differentiate w.r.t. c_9

$$10080c_{9}$$

Steps Using Definition of a Derivative

Cancel out 9^{7} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}c_{9}}(7!c_{9}^{2})$$

The factorial of 7 is 5040.

$$\frac{\mathrm{d}}{\mathrm{d}c_{9}}(5040c_{9}^{2})$$

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

$$2\times 5040c_{9}^{2-1}$$

Multiply 2 times 5040.

$$10080c_{9}^{2-1}$$

Subtract 1 from 2.

$$10080c_{9}^{1}$$

For any term t, t^{1}=t.

$$10080c_{9}$$