Solve 400g(350g)(300g)

$$400 g ( 350 g ) ( 300 g )$$

Evaluate

$$42000000g^{3}$$

Solution Steps

Multiply g and g to get g^{2}.

$$400g^{2}\times 350\times 300g$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$400g^{3}\times 350\times 300$$

Multiply 400 and 350 to get 140000.

$$140000g^{3}\times 300$$

Multiply 140000 and 300 to get 42000000.

$$42000000g^{3}$$

Differentiate w.r.t. g

$$126000000g^{2}$$

Steps Using Definition of a Derivative

Multiply g and g to get g^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}g}(400g^{2}\times 350\times 300g)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}g}(400g^{3}\times 350\times 300)$$

Multiply 400 and 350 to get 140000.

$$\frac{\mathrm{d}}{\mathrm{d}g}(140000g^{3}\times 300)$$

Multiply 140000 and 300 to get 42000000.

$$\frac{\mathrm{d}}{\mathrm{d}g}(42000000g^{3})$$

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

$$3\times 42000000g^{3-1}$$

Multiply 3 times 42000000.

$$126000000g^{3-1}$$

Subtract 1 from 3.

$$126000000g^{2}$$