Solve 35x^21*22/2

$$\frac{ 35 { x }^{ } 21 \times 22 }{ 2 }$$

Evaluate

$$8085x$$

Solution Steps

Calculate x to the power of 1 and get x.

$$\frac{35x\times 21\times 22}{2}$$

Multiply 35 and 21 to get 735.

$$\frac{735x\times 22}{2}$$

Multiply 735 and 22 to get 16170.

$$\frac{16170x}{2}$$

Divide 16170x by 2 to get 8085x.

$$8085x$$

Differentiate w.r.t. x

$$8085$$

Steps Using Definition of a Derivative

Calculate x to the power of 1 and get x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{35x\times 21\times 22}{2})$$

Multiply 35 and 21 to get 735.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{735x\times 22}{2})$$

Multiply 735 and 22 to get 16170.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{16170x}{2})$$

Divide 16170x by 2 to get 8085x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8085x)$$

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

$$8085x^{1-1}$$

Subtract 1 from 1.

$$8085x^{0}$$

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

$$8085\times 1$$

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

$$8085$$