Solve 25x^3-10^2+x=

$$25 x ^ { 3 } - 10 ^ { 2 } + x =$$

Differentiate w.r.t. x

$$75x^{2}+1$$

Steps Using Derivative Rule for Sum

Calculate 10 to the power of 2 and get 100.

$$\frac{\mathrm{d}}{\mathrm{d}x}(25x^{3}-100+x)$$

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}.

$$3\times 25x^{3-1}+x^{1-1}$$

Multiply 3 times 25.

$$75x^{3-1}+x^{1-1}$$

Subtract 1 from 3.

$$75x^{2}+x^{1-1}$$

Subtract 1 from 1.

$$75x^{2}+x^{0}$$

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

$$75x^{2}+1$$

Evaluate

$$25x^{3}+x-100$$

Solution Steps

Calculate 10 to the power of 2 and get 100.

$$25x^{3}-100+x$$