Solve 3a^2*(-4a^5)*(1/6a^3)=

$$3 a ^ { 2 } \cdot ( - 4 a ^ { 5 } ) \cdot ( \frac { 1 } { 6 } a ^ { 3 } ) =$$

Evaluate

$$-2a^{10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$3a^{7}\left(-4\right)\times \frac{1}{6}a^{3}$$

To multiply powers of the same base, add their exponents. Add 7 and 3 to get 10.

$$3a^{10}\left(-4\right)\times \frac{1}{6}$$

Multiply 3 and -4 to get -12.

$$-12a^{10}\times \frac{1}{6}$$

Multiply -12 and \frac{1}{6} to get -2.

$$-2a^{10}$$

Differentiate w.r.t. a

$$-20a^{9}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}a}(3a^{7}\left(-4\right)\times \frac{1}{6}a^{3})$$

To multiply powers of the same base, add their exponents. Add 7 and 3 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}a}(3a^{10}\left(-4\right)\times \frac{1}{6})$$

Multiply 3 and -4 to get -12.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-12a^{10}\times \frac{1}{6})$$

Multiply -12 and \frac{1}{6} to get -2.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-2a^{10})$$

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

$$10\left(-2\right)a^{10-1}$$

Multiply 10 times -2.

$$-20a^{10-1}$$

Subtract 1 from 10.

$$-20a^{9}$$