Solve d/dx(4x^2-5x^3+16x)

$$\frac { d } { d x } ( 4 x ^ { 2 } - 5 x ^ { 3 } + 16 x )$$

Evaluate

$$\left(-5x-4\right)\left(3x-4\right)$$

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}.

$$2\times 4x^{2-1}+3\left(-5\right)x^{3-1}+16x^{1-1}$$

Multiply 2 times 4.

$$8x^{2-1}+3\left(-5\right)x^{3-1}+16x^{1-1}$$

Subtract 1 from 2.

$$8x^{1}+3\left(-5\right)x^{3-1}+16x^{1-1}$$

Multiply 3 times -5.

$$8x^{1}-15x^{3-1}+16x^{1-1}$$

Subtract 1 from 3.

$$8x^{1}-15x^{2}+16x^{1-1}$$

Subtract 1 from 1.

$$8x^{1}-15x^{2}+16x^{0}$$

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

$$8x-15x^{2}+16x^{0}$$

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

$$8x-15x^{2}+16\times 1$$

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

$$8x-15x^{2}+16$$

Differentiate w.r.t. x

$$8-30x$$