Solve 10a^4*a^6*a^3

$$10 a ^ { 4 } \cdot a ^ { 6 } \cdot a ^ { 3 }$$

Evaluate

$$10a^{13}$$

Solution Steps

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

$$10a^{10}a^{3}$$

To multiply powers of the same base, add their exponents. Add 10 and 3 to get 13.

$$10a^{13}$$

Differentiate w.r.t. a

$$130a^{12}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(10a^{10}a^{3})$$

To multiply powers of the same base, add their exponents. Add 10 and 3 to get 13.

$$\frac{\mathrm{d}}{\mathrm{d}a}(10a^{13})$$

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

$$13\times 10a^{13-1}$$

Multiply 13 times 10.

$$130a^{13-1}$$

Subtract 1 from 13.

$$130a^{12}$$