Solve 2a^4+9a^4-7a^4+6a^4

$$2 a ^ { 4 } + 9 a ^ { 4 } - 7 a ^ { 4 } + 6 a ^ { 4 }$$

Evaluate

$$10a^{4}$$

Solution Steps

Combine 2a^{4} and 9a^{4} to get 11a^{4}.

$$11a^{4}-7a^{4}+6a^{4}$$

Combine 11a^{4} and -7a^{4} to get 4a^{4}.

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

Combine 4a^{4} and 6a^{4} to get 10a^{4}.

$$10a^{4}$$

Differentiate w.r.t. a

$$40a^{3}$$

Steps Using Definition of a Derivative

Combine 2a^{4} and 9a^{4} to get 11a^{4}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(11a^{4}-7a^{4}+6a^{4})$$

Combine 11a^{4} and -7a^{4} to get 4a^{4}.

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

Combine 4a^{4} and 6a^{4} to get 10a^{4}.

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

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

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

Multiply 4 times 10.

$$40a^{4-1}$$

Subtract 1 from 4.

$$40a^{3}$$