Solve 8a^2*a^4diva^3-6a^3

$$8 a ^ { 2 } \cdot a ^ { 4 } \div a ^ { 3 } - 6 a ^ { 3 }$$

Evaluate

$$2a^{3}$$

Solution Steps

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

$$\frac{8a^{6}}{a^{3}}-6a^{3}$$

Cancel out a^{3} in both numerator and denominator.

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

Combine 8a^{3} and -6a^{3} to get 2a^{3}.

$$2a^{3}$$

Differentiate w.r.t. a

$$6a^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{8a^{6}}{a^{3}}-6a^{3})$$

Cancel out a^{3} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(8a^{3}-6a^{3})$$

Combine 8a^{3} and -6a^{3} to get 2a^{3}.

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

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

$$3\times 2a^{3-1}$$

Multiply 3 times 2.

$$6a^{3-1}$$

Subtract 1 from 3.

$$6a^{2}$$