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

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

Evaluate

$$-20x^{12}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$\left(-4\right)^{1}x^{3}x^{5}\times 5^{1}x^{1}x^{3}$$

Use the Commutative Property of Multiplication.

$$\left(-4\right)^{1}\times 5^{1}x^{3}x^{1}x^{5}x^{3}$$

To multiply powers of the same base, add their exponents.

$$\left(-4\right)^{1}\times 5^{1}x^{3+1}x^{5+3}$$

Add the exponents 3 and 1.

$$\left(-4\right)^{1}\times 5^{1}x^{4}x^{5+3}$$

Add the exponents 5 and 3.

$$\left(-4\right)^{1}\times 5^{1}x^{4}x^{8}$$

Multiply -4 times 5.

$$-20x^{4}x^{8}$$

Differentiate w.r.t. x

$$-240x^{11}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-4x^{8}\times 5xx^{3})$$

To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-4x^{9}\times 5x^{3})$$

To multiply powers of the same base, add their exponents. Add 9 and 3 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-4x^{12}\times 5)$$

Multiply -4 and 5 to get -20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-20x^{12})$$

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

$$12\left(-20\right)x^{12-1}$$

Multiply 12 times -20.

$$-240x^{12-1}$$

Subtract 1 from 12.

$$-240x^{11}$$