Solve 10g^5*3g^4div12g^12

$$10 g ^ { 5 } \times 3 g ^ { 4 } \div 12 g ^ { 12 }$$

Evaluate

$$\frac{5g^{21}}{2}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 4 to get 9.

$$\frac{10g^{9}\times 3}{12}g^{12}$$

Multiply 10 and 3 to get 30.

$$\frac{30g^{9}}{12}g^{12}$$

Divide 30g^{9} by 12 to get \frac{5}{2}g^{9}.

$$\frac{5}{2}g^{9}g^{12}$$

To multiply powers of the same base, add their exponents. Add 9 and 12 to get 21.

$$\frac{5}{2}g^{21}$$

Differentiate w.r.t. g

$$\frac{105g^{20}}{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 4 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{10g^{9}\times 3}{12}g^{12})$$

Multiply 10 and 3 to get 30.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{30g^{9}}{12}g^{12})$$

Divide 30g^{9} by 12 to get \frac{5}{2}g^{9}.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{5}{2}g^{9}g^{12})$$

To multiply powers of the same base, add their exponents. Add 9 and 12 to get 21.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{5}{2}g^{21})$$

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

$$21\times \frac{5}{2}g^{21-1}$$

Multiply 21 times \frac{5}{2}.

$$\frac{105}{2}g^{21-1}$$

Subtract 1 from 21.

$$\frac{105}{2}g^{20}$$