Solve x^-3*x^6*x^4*x^-5

$$x ^ { - 3 } \cdot x ^ { 6 } \cdot x ^ { 4 } \cdot x ^ { - 5 }$$

Evaluate

$$x^{2}$$

Solution Steps

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

$$x^{3}x^{4}x^{-5}$$

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

$$x^{7}x^{-5}$$

To multiply powers of the same base, add their exponents. Add 7 and -5 to get 2.

$$x^{2}$$

Differentiate w.r.t. x

$$2x$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}x^{4}x^{-5})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{7}x^{-5})$$

To multiply powers of the same base, add their exponents. Add 7 and -5 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2})$$

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

$$2x^{2-1}$$

Subtract 1 from 2.

$$2x^{1}$$

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

$$2x$$