Solve 6x(96x^3/1)

$$6x( \frac{ 96 { x }^{ 3 } }{ 1 } )$$

Evaluate

$$576x^{4}$$

Solution Steps

Anything divided by one gives itself.

$$6x\times 96x^{3}$$

Multiply 6 and 96 to get 576.

$$576xx^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$576x^{4}$$

Differentiate w.r.t. x

$$2304x^{3}$$

Steps Using Definition of a Derivative

Anything divided by one gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x\times 96x^{3})$$

Multiply 6 and 96 to get 576.

$$\frac{\mathrm{d}}{\mathrm{d}x}(576xx^{3})$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(576x^{4})$$

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

$$4\times 576x^{4-1}$$

Multiply 4 times 576.

$$2304x^{4-1}$$

Subtract 1 from 4.

$$2304x^{3}$$