Solve (-3x^4)(5x^2)(-2x^5)

$$( - 3 x ^ { 4 } ) ( 5 x ^ { 2 } ) ( - 2 x ^ { 5 } )$$

Evaluate

$$30x^{11}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$-3x^{6}\times 5\left(-2\right)x^{5}$$

To multiply powers of the same base, add their exponents. Add 6 and 5 to get 11.

$$-3x^{11}\times 5\left(-2\right)$$

Multiply -3 and 5 to get -15.

$$-15x^{11}\left(-2\right)$$

Multiply -15 and -2 to get 30.

$$30x^{11}$$

Differentiate w.r.t. x

$$330x^{10}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-3x^{6}\times 5\left(-2\right)x^{5})$$

To multiply powers of the same base, add their exponents. Add 6 and 5 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-3x^{11}\times 5\left(-2\right))$$

Multiply -3 and 5 to get -15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-15x^{11}\left(-2\right))$$

Multiply -15 and -2 to get 30.

$$\frac{\mathrm{d}}{\mathrm{d}x}(30x^{11})$$

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

$$11\times 30x^{11-1}$$

Multiply 11 times 30.

$$330x^{11-1}$$

Subtract 1 from 11.

$$330x^{10}$$