Solve -1^-7x^33x^-2

$${ -1 }^{ -7 } { x }^{ 3 } 3 { x }^{ -2 }$$

Evaluate

$$-3x$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and -2 to get 1.

$$\left(-1\right)^{-7}x^{1}\times 3$$

Calculate -1 to the power of -7 and get -1.

$$-x^{1}\times 3$$

Calculate x to the power of 1 and get x.

$$-x\times 3$$

Multiply -1 and 3 to get -3.

$$-3x$$

Differentiate w.r.t. x

$$-3$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and -2 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-1\right)^{-7}x^{1}\times 3)$$

Calculate -1 to the power of -7 and get -1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-x^{1}\times 3)$$

Calculate x to the power of 1 and get x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-x\times 3)$$

Multiply -1 and 3 to get -3.

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

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

$$-3x^{1-1}$$

Subtract 1 from 1.

$$-3x^{0}$$

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

$$-3$$