Solve 32x/100*32/1

$$\frac { 32 x } { 100 } \times \frac { 32 } { 1 }$$

Evaluate

$$\frac{256x}{25}$$

Solution Steps

Divide 32x by 100 to get \frac{8}{25}x.

$$\frac{8}{25}x\times \frac{32}{1}$$

Anything divided by one gives itself.

$$\frac{8}{25}x\times 32$$

Express \frac{8}{25}\times 32 as a single fraction.

$$\frac{8\times 32}{25}x$$

Multiply 8 and 32 to get 256.

$$\frac{256}{25}x$$

Differentiate w.r.t. x

$$\frac{256}{25} = 10\frac{6}{25} = 10.24$$

Steps Using Definition of a Derivative

Divide 32x by 100 to get \frac{8}{25}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8}{25}x\times \frac{32}{1})$$

Anything divided by one gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8}{25}x\times 32)$$

Express \frac{8}{25}\times 32 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8\times 32}{25}x)$$

Multiply 8 and 32 to get 256.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{256}{25}x)$$

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

$$\frac{256}{25}x^{1-1}$$

Subtract 1 from 1.

$$\frac{256}{25}x^{0}$$

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

$$\frac{256}{25}\times 1$$

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

$$\frac{256}{25}$$