Solve d/dxleft(25x^4-15x^3+xyright)

$$\frac{d}{d x } \left(25 { x }^{ 4 } -15 { x }^{ 3 } +xy \right)$$

Evaluate

$$100x^{3}-45x^{2}+y$$

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}.

$$4\times 25x^{4-1}+3\left(-15\right)x^{3-1}+yx^{1-1}$$

Multiply 4 times 25.

$$100x^{4-1}+3\left(-15\right)x^{3-1}+yx^{1-1}$$

Subtract 1 from 4.

$$100x^{3}+3\left(-15\right)x^{3-1}+yx^{1-1}$$

Multiply 3 times -15.

$$100x^{3}-45x^{3-1}+yx^{1-1}$$

Subtract 1 from 3.

$$100x^{3}-45x^{2}+yx^{1-1}$$

Subtract 1 from 1.

$$100x^{3}-45x^{2}+yx^{0}$$

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

$$100x^{3}-45x^{2}+y\times 1$$

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

$$100x^{3}-45x^{2}+y$$

Differentiate w.r.t. x

$$30x\left(10x-3\right)$$