Solve (-a^3)*a^3*(-a^4)

$$( - a ^ { 3 } ) \cdot a ^ { 3 } \cdot ( - a ^ { 4 } )$$

Evaluate

$$a^{10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$-a^{6}\left(-1\right)a^{4}$$

Multiply -1 and -1 to get 1.

$$a^{6}a^{4}$$

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$a^{10}$$

Differentiate w.r.t. a

$$10a^{9}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

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

Multiply -1 and -1 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{6}a^{4})$$

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

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

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

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

Subtract 1 from 10.

$$10a^{9}$$