Solve (a^2)^3-2(a^2)^2+20

$$( a ^ { 2 } ) ^ { 3 } - 2 ( a ^ { 2 } ) ^ { 2 } + 20$$

Evaluate

$$a^{6}-2a^{4}+20$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$a^{6}-2\left(a^{2}\right)^{2}+20$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$a^{6}-2a^{4}+20$$

Differentiate w.r.t. a

$$6a^{5}-8a^{3}$$

Steps Using Derivative Rule for Sum

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{6}-2\left(a^{2}\right)^{2}+20)$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{6}-2a^{4}+20)$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$6a^{6-1}+4\left(-2\right)a^{4-1}$$

Subtract 1 from 6.

$$6a^{5}+4\left(-2\right)a^{4-1}$$

Multiply 4 times -2.

$$6a^{5}-8a^{4-1}$$

Subtract 1 from 4.

$$6a^{5}-8a^{3}$$