Solve 7(x^3)^2+x^4x^2

$$7 ( x ^ { 3 } ) ^ { 2 } + x ^ { 4 } x ^ { 2 }$$

Evaluate

$$8x^{6}$$

Solution Steps

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

$$7x^{6}+x^{4}x^{2}$$

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

$$7x^{6}+x^{6}$$

Combine 7x^{6} and x^{6} to get 8x^{6}.

$$8x^{6}$$

Differentiate w.r.t. x

$$48x^{5}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{6}+x^{4}x^{2})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{6}+x^{6})$$

Combine 7x^{6} and x^{6} to get 8x^{6}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{6})$$

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

$$6\times 8x^{6-1}$$

Multiply 6 times 8.

$$48x^{6-1}$$

Subtract 1 from 6.

$$48x^{5}$$