Solve 2x^2*38x^2=

$$2 { x }^{ 2 } \times 38 { x }^{ 2 } =$$

Evaluate

$$76x^{4}$$

Solution Steps

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

$$2x^{4}\times 38$$

Multiply 2 and 38 to get 76.

$$76x^{4}$$

Differentiate w.r.t. x

$$304x^{3}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{4}\times 38)$$

Multiply 2 and 38 to get 76.

$$\frac{\mathrm{d}}{\mathrm{d}x}(76x^{4})$$

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

$$4\times 76x^{4-1}$$

Multiply 4 times 76.

$$304x^{4-1}$$

Subtract 1 from 4.

$$304x^{3}$$