Solve (1)x*x^3+x^2*x^2

$$( 1 ) x \cdot x ^ { 3 } + x ^ { 2 } \cdot x ^ { 2 }$$

Evaluate

$$2x^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$1x^{4}+x^{2}x^{2}$$

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

$$1x^{4}+x^{4}$$

Combine 1x^{4} and x^{4} to get 2x^{4}.

$$2x^{4}$$

Differentiate w.r.t. x

$$8x^{3}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(1x^{4}+x^{2}x^{2})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(1x^{4}+x^{4})$$

Combine 1x^{4} and x^{4} to get 2x^{4}.

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

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

$$4\times 2x^{4-1}$$

Multiply 4 times 2.

$$8x^{4-1}$$

Subtract 1 from 4.

$$8x^{3}$$