Solve 2(a^2)^6-(a^3)^4quad4)

$$2 ( a ^ { 2 } ) ^ { 6 } - ( a ^ { 3 } ) ^ { 4 } \quad 4 )$$

Evaluate

$$-2a^{12}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 6 to get 12.

$$2a^{12}-\left(a^{3}\right)^{4}\times 4$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$2a^{12}-a^{12}\times 4$$

Combine 2a^{12} and -a^{12}\times 4 to get -2a^{12}.

$$-2a^{12}$$

Differentiate w.r.t. a

$$-24a^{11}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 2 and 6 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}a}(2a^{12}-\left(a^{3}\right)^{4}\times 4)$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}a}(2a^{12}-a^{12}\times 4)$$

Combine 2a^{12} and -a^{12}\times 4 to get -2a^{12}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-2a^{12})$$

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

$$12\left(-2\right)a^{12-1}$$

Multiply 12 times -2.

$$-24a^{12-1}$$

Subtract 1 from 12.

$$-24a^{11}$$