Solve 6x2^25^2

$$6x { 2 }^{ 2 } { 5 }^{ 2 }$$

Evaluate

$$600x$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$6x\times 4\times 5^{2}$$

Multiply 6 and 4 to get 24.

$$24x\times 5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$24x\times 25$$

Multiply 24 and 25 to get 600.

$$600x$$

Differentiate w.r.t. x

$$600$$

Steps Using Definition of a Derivative

Calculate 2 to the power of 2 and get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x\times 4\times 5^{2})$$

Multiply 6 and 4 to get 24.

$$\frac{\mathrm{d}}{\mathrm{d}x}(24x\times 5^{2})$$

Calculate 5 to the power of 2 and get 25.

$$\frac{\mathrm{d}}{\mathrm{d}x}(24x\times 25)$$

Multiply 24 and 25 to get 600.

$$\frac{\mathrm{d}}{\mathrm{d}x}(600x)$$

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

$$600x^{1-1}$$

Subtract 1 from 1.

$$600x^{0}$$

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

$$600\times 1$$

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

$$600$$