Solve 99*35*140*28/7*30*165*315k

$$\frac { 99 \cdot 35 \cdot 140 \cdot 28 } { 7 \cdot 30 \cdot 165 \cdot 315 } k$$

Evaluate

$$\frac{56k}{45}$$

Solution Steps

Cancel out 2\times 3\times 5\times 5\times 7\times 7\times 33 in both numerator and denominator.

$$\frac{2\times 28}{45}k$$

Multiply 2 and 28 to get 56.

$$\frac{56}{45}k$$

Differentiate w.r.t. k

$$\frac{56}{45} = 1\frac{11}{45} = 1.2444444444444445$$

Steps Using Definition of a Derivative

Cancel out 2\times 3\times 5\times 5\times 7\times 7\times 33 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{2\times 28}{45}k)$$

Multiply 2 and 28 to get 56.

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{56}{45}k)$$

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

$$\frac{56}{45}k^{1-1}$$

Subtract 1 from 1.

$$\frac{56}{45}k^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{56}{45}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{56}{45}$$