Solve (7a)(-a)(5a^2)

$$( 7 a ) ( - a ) ( 5 a ^ { 2 } )$$

Evaluate

$$-35a^{4}$$

Solution Steps

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

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

Multiply 7 and 5 to get 35.

$$35a^{3}\left(-a\right)$$

Multiply 35 and -1 to get -35.

$$-35a^{3}a$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$-35a^{4}$$

Differentiate w.r.t. a

$$-140a^{3}$$

Steps Using Definition of a Derivative

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

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

Multiply 7 and 5 to get 35.

$$\frac{\mathrm{d}}{\mathrm{d}a}(35a^{3}\left(-a\right))$$

Multiply 35 and -1 to get -35.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-35a^{3}a)$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-35a^{4})$$

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

$$4\left(-35\right)a^{4-1}$$

Multiply 4 times -35.

$$-140a^{4-1}$$

Subtract 1 from 4.

$$-140a^{3}$$