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

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

Evaluate

$$60a^{7}$$

Solution Steps

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

$$4a^{3}\left(-3\right)\left(-5\right)a^{4}$$

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

$$4a^{7}\left(-3\right)\left(-5\right)$$

Multiply 4 and -3 to get -12.

$$-12a^{7}\left(-5\right)$$

Multiply -12 and -5 to get 60.

$$60a^{7}$$

Differentiate w.r.t. a

$$420a^{6}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(4a^{3}\left(-3\right)\left(-5\right)a^{4})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(4a^{7}\left(-3\right)\left(-5\right))$$

Multiply 4 and -3 to get -12.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-12a^{7}\left(-5\right))$$

Multiply -12 and -5 to get 60.

$$\frac{\mathrm{d}}{\mathrm{d}a}(60a^{7})$$

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

$$7\times 60a^{7-1}$$

Multiply 7 times 60.

$$420a^{7-1}$$

Subtract 1 from 7.

$$420a^{6}$$