Solve 54x^336x^3

$$54 x ^ { 3 } 36 x ^ { 3 }$$

Evaluate

$$1944x^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$54x^{6}\times 36$$

Multiply 54 and 36 to get 1944.

$$1944x^{6}$$

Differentiate w.r.t. x

$$11664x^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(54x^{6}\times 36)$$

Multiply 54 and 36 to get 1944.

$$\frac{\mathrm{d}}{\mathrm{d}x}(1944x^{6})$$

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

$$6\times 1944x^{6-1}$$

Multiply 6 times 1944.

$$11664x^{6-1}$$

Subtract 1 from 6.

$$11664x^{5}$$