Solve -3a^4*a^2-4a^6

$$- 3 a ^ { 4 } \times a ^ { 2 } - 4 a ^ { 6 }$$

Evaluate

$$-7a^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$-3a^{6}-4a^{6}$$

Combine -3a^{6} and -4a^{6} to get -7a^{6}.

$$-7a^{6}$$

Differentiate w.r.t. a

$$-42a^{5}$$

Steps Using Derivative Rule for Sum

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}.

$$4\left(-3a^{2}\right)a^{4-1}+6\left(-4\right)a^{6-1}$$

Multiply 4 times -3a^{2}.

$$\left(-12a^{2}\right)a^{4-1}+6\left(-4\right)a^{6-1}$$

Subtract 1 from 4.

$$\left(-12a^{2}\right)a^{3}+6\left(-4\right)a^{6-1}$$

Multiply 6 times -4.

$$\left(-12a^{2}\right)a^{3}-24a^{6-1}$$

Subtract 1 from 6.

$$\left(-12a^{2}\right)a^{3}-24a^{5}$$