Solve (x^2)^3+2x^2*x^4

$$( x ^ { 2 } ) ^ { 3 } + 2 x ^ { 2 } \cdot x ^ { 4 }$$

Evaluate

$$3x^{6}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$x^{6}+2x^{2}x^{4}$$

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

$$x^{6}+2x^{6}$$

Combine x^{6} and 2x^{6} to get 3x^{6}.

$$3x^{6}$$

Differentiate w.r.t. x

$$18x^{5}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{6}+2x^{2}x^{4})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{6}+2x^{6})$$

Combine x^{6} and 2x^{6} to get 3x^{6}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{6})$$

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

$$6\times 3x^{6-1}$$

Multiply 6 times 3.

$$18x^{6-1}$$

Subtract 1 from 6.

$$18x^{5}$$