Solve (-1)^-4(x^3)(3x^2)(-1)^-3

$$( - 1 ) ^ { - 4 } ( x ^ { 3 } ) ( 3 x ^ { 2 } ) ( - 1 ) ^ { - 3 }$$

Evaluate

$$-3x^{5}$$

Solution Steps

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

$$\left(-1\right)^{-7}x^{3}\times 3x^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\left(-1\right)^{-7}x^{5}\times 3$$

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

$$-x^{5}\times 3$$

Multiply -1 and 3 to get -3.

$$-3x^{5}$$

Differentiate w.r.t. x

$$-15x^{4}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-1\right)^{-7}x^{3}\times 3x^{2})$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-1\right)^{-7}x^{5}\times 3)$$

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

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

Multiply -1 and 3 to get -3.

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

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

$$5\left(-3\right)x^{5-1}$$

Multiply 5 times -3.

$$-15x^{5-1}$$

Subtract 1 from 5.

$$-15x^{4}$$