Solve 2^3*a^3*5a^4

$$2 ^ { 3 } \times a ^ { 3 } \times 5 a ^ { 4 }$$

Evaluate

$$40a^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$2^{3}a^{7}\times 5$$

Calculate 2 to the power of 3 and get 8.

$$8a^{7}\times 5$$

Multiply 8 and 5 to get 40.

$$40a^{7}$$

Differentiate w.r.t. a

$$280a^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}a}(2^{3}a^{7}\times 5)$$

Calculate 2 to the power of 3 and get 8.

$$\frac{\mathrm{d}}{\mathrm{d}a}(8a^{7}\times 5)$$

Multiply 8 and 5 to get 40.

$$\frac{\mathrm{d}}{\mathrm{d}a}(40a^{7})$$

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

$$7\times 40a^{7-1}$$

Multiply 7 times 40.

$$280a^{7-1}$$

Subtract 1 from 7.

$$280a^{6}$$