Solve (6^{4}x^3)(6^-4x^4)(x^-6)

$$( 6 ^ { 4 } x ^ { 3 } ) ( 6 ^ { - 4 } x ^ { 4 } ) ( x ^ { - 6 } )$$

Evaluate

$$x$$

Solution Steps

Multiply 6^{4} and 6^{-4} to get 1.

$$x^{3}x^{4}x^{-6}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$x^{7}x^{-6}$$

To multiply powers of the same base, add their exponents. Add 7 and -6 to get 1.

$$x^{1}$$

Calculate x to the power of 1 and get x.

$$x$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

Multiply 6^{4} and 6^{-4} to get 1.

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

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{7}x^{-6})$$

To multiply powers of the same base, add their exponents. Add 7 and -6 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{1})$$

Calculate x to the power of 1 and get x.

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

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

$$x^{1-1}$$

Subtract 1 from 1.

$$x^{0}$$

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

$$1$$