Solve =16x^6*64x^6

$$= 16 x ^ { 6 } \cdot 64 x ^ { 6 }$$

Evaluate

$$1024x^{12}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$16x^{12}\times 64$$

Multiply 16 and 64 to get 1024.

$$1024x^{12}$$

Differentiate w.r.t. x

$$12288x^{11}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(16x^{12}\times 64)$$

Multiply 16 and 64 to get 1024.

$$\frac{\mathrm{d}}{\mathrm{d}x}(1024x^{12})$$

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

$$12\times 1024x^{12-1}$$

Multiply 12 times 1024.

$$12288x^{12-1}$$

Subtract 1 from 12.

$$12288x^{11}$$