Solve 2xx^2+14x+45^2

$$2 x x ^ { 2 } + 14 x + 45 ^ { 2 }$$

Evaluate

$$2x^{3}+14x+2025$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$2x^{3}+14x+45^{2}$$

Calculate 45 to the power of 2 and get 2025.

$$2x^{3}+14x+2025$$

Differentiate w.r.t. x

$$6x^{2}+14$$

Steps Using Derivative Rule for Sum

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3}+14x+45^{2})$$

Calculate 45 to the power of 2 and get 2025.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3}+14x+2025)$$

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}.

$$3\times 2x^{3-1}+14x^{1-1}$$

Multiply 3 times 2.

$$6x^{3-1}+14x^{1-1}$$

Subtract 1 from 3.

$$6x^{2}+14x^{1-1}$$

Subtract 1 from 1.

$$6x^{2}+14x^{0}$$

For any term t except 0, t^{0}=1.

$$6x^{2}+14\times 1$$

For any term t, t\times 1=t and 1t=t.

$$6x^{2}+14$$