Solve 3(2x4^3)/4=

$$\frac { 3 ( 2 x 4 ^ { 3 } ) } { 4 } =$$

Evaluate

$$96x$$

Solution Steps

Multiply 3 and 2 to get 6.

$$\frac{6x\times 4^{3}}{4}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{6x\times 64}{4}$$

Multiply 6 and 64 to get 384.

$$\frac{384x}{4}$$

Divide 384x by 4 to get 96x.

$$96x$$

Differentiate w.r.t. x

$$96$$

Steps Using Definition of a Derivative

Multiply 3 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6x\times 4^{3}}{4})$$

Calculate 4 to the power of 3 and get 64.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6x\times 64}{4})$$

Multiply 6 and 64 to get 384.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{384x}{4})$$

Divide 384x by 4 to get 96x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(96x)$$

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

$$96x^{1-1}$$

Subtract 1 from 1.

$$96x^{0}$$

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

$$96\times 1$$

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

$$96$$