Solve {c}{17x^2+11}{+8x^2+11}

$$\left. \begin{array} { c } { 17 x ^ { 2 } + 11 } \\ { + 8 x ^ { 2 } + 11 } \end{array} \right.$$

Evaluate

$$25x^{2}+22$$

Solution Steps

Combine 17x^{2} and 8x^{2} to get 25x^{2}.

$$25x^{2}+11+11$$

Add 11 and 11 to get 22.

$$25x^{2}+22$$

Differentiate w.r.t. x

$$50x$$

Steps Using Derivative Rule for Sum

Combine 17x^{2} and 8x^{2} to get 25x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(25x^{2}+11+11)$$

Add 11 and 11 to get 22.

$$\frac{\mathrm{d}}{\mathrm{d}x}(25x^{2}+22)$$

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}.

$$2\times 25x^{2-1}$$

Multiply 2 times 25.

$$50x^{2-1}$$

Subtract 1 from 2.

$$50x^{1}$$

For any term t, t^{1}=t.

$$50x$$