Solve x^{2}*x^{4}*x^{6}+(x^2)^2+[(-11)^4]^3

$$x ^ { 2 } \cdot x ^ { 4 } \cdot x ^ { 6 } + ( x ^ { 2 } ) ^ { 2 } + [ ( - 11 ) ^ { 4 } ] ^ { 3 }$$

Evaluate

$$x^{12}+x^{4}[phone]$$

Solution Steps

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

$$x^{6}x^{6}+\left(x^{2}\right)^{2}+\left(\left(-11\right)^{4}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$x^{12}+\left(x^{2}\right)^{2}+\left(\left(-11\right)^{4}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$x^{12}+x^{4}+\left(\left(-11\right)^{4}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$x^{12}+x^{4}+\left(-11\right)^{12}$$

Calculate -11 to the power of 12 and get 3138428376721.

$$x^{12}+x^{4}[phone]$$

Differentiate w.r.t. x

$$12x^{11}+4x^{3}$$

Steps Using Derivative Rule for Sum

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{6}x^{6}+\left(x^{2}\right)^{2}+\left(\left(-11\right)^{4}\right)^{3})$$

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{12}+\left(x^{2}\right)^{2}+\left(\left(-11\right)^{4}\right)^{3})$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{12}+x^{4}+\left(\left(-11\right)^{4}\right)^{3})$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{12}+x^{4}+\left(-11\right)^{12})$$

Calculate -11 to the power of 12 and get 3138428376721.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{12}+x^{4}[phone])$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$12x^{12-1}+4x^{4-1}$$

Subtract 1 from 12.

$$12x^{11}+4x^{4-1}$$

Subtract 1 from 4.

$$12x^{11}+4x^{3}$$