Solve 2*6x+left(4^2right)^3x

$$2 \times 6x+ { \left( { 4 }^{ 2 } \right) }^{ 3 } x$$

Evaluate

$$4108x$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

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

Multiply 2 and 6 to get 12.

$$12x+4^{6}x$$

Calculate 4 to the power of 6 and get 4096.

$$12x+4096x$$

Combine 12x and 4096x to get 4108x.

$$4108x$$

Differentiate w.r.t. x

$$4108$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

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

Multiply 2 and 6 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x+4^{6}x)$$

Calculate 4 to the power of 6 and get 4096.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x+4096x)$$

Combine 12x and 4096x to get 4108x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4108x)$$

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

$$4108x^{1-1}$$

Subtract 1 from 1.

$$4108x^{0}$$

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

$$4108\times 1$$

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

$$4108$$