Solve d/dx(4x^2+5x^3+8x^6+2)

$$\frac { d } { d x } ( 4 x ^ { 2 } + 5 x ^ { 3 } + 8 x ^ { 6 } + 2 )$$

Evaluate

$$x\left(48x^{4}+15x+8\right)$$

Steps Using Derivative Rule for Sum

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}.

$$2\times 4x^{2-1}+3\times 5x^{3-1}+6\times 8x^{6-1}$$

Multiply 2 times 4.

$$8x^{2-1}+3\times 5x^{3-1}+6\times 8x^{6-1}$$

Subtract 1 from 2.

$$8x^{1}+3\times 5x^{3-1}+6\times 8x^{6-1}$$

Multiply 3 times 5.

$$8x^{1}+15x^{3-1}+6\times 8x^{6-1}$$

Subtract 1 from 3.

$$8x^{1}+15x^{2}+6\times 8x^{6-1}$$

Multiply 3 times 5.

$$8x^{1}+15x^{2}+48x^{6-1}$$

Subtract 1 from 6.

$$8x^{1}+15x^{2}+48x^{5}$$

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

$$8x+15x^{2}+48x^{5}$$

Differentiate w.r.t. x

$$240x^{4}+30x+8$$