Solve d/dxleft(25x^4-12x^3+x^2yright)

$$\frac{d}{d x } \left(25 { x }^{ 4 } -12 { x }^{ 3 } + { x }^{ 2 } y \right)$$

Evaluate

$$2x\left(50x^{2}-18x+y\right)$$

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}.

$$4\times 25x^{4-1}+3\left(-12\right)x^{3-1}+2yx^{2-1}$$

Multiply 4 times 25.

$$100x^{4-1}+3\left(-12\right)x^{3-1}+2yx^{2-1}$$

Subtract 1 from 4.

$$100x^{3}+3\left(-12\right)x^{3-1}+2yx^{2-1}$$

Multiply 3 times -12.

$$100x^{3}-36x^{3-1}+2yx^{2-1}$$

Subtract 1 from 3.

$$100x^{3}-36x^{2}+2yx^{2-1}$$

Subtract 1 from 2.

$$100x^{3}-36x^{2}+2yx^{1}$$

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

$$100x^{3}-36x^{2}+2yx$$

Differentiate w.r.t. x

$$2\left(150x^{2}-36x+y\right)$$