Solve a*4a^9

$$a \cdot 4 a ^ { 9 }$$

Differentiate w.r.t. a

$$40a^{9}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 9 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{10}\times 4)$$

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

$$10\times 4a^{10-1}$$

Multiply 10 times 4.

$$40a^{10-1}$$

Subtract 1 from 10.

$$40a^{9}$$

Evaluate

$$4a^{10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 9 to get 10.

$$a^{10}\times 4$$