Solve 2x^3+5x^3+x-27=

$$2 x ^ { 3 } + 5 x ^ { 3 } + x - 27 =$$

Differentiate w.r.t. x

$$21x^{2}+1$$

Steps Using Derivative Rule for Sum

Combine 2x^{3} and 5x^{3} to get 7x^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{3}+x-27)$$

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}.

$$3\times 7x^{3-1}+x^{1-1}$$

Multiply 3 times 7.

$$21x^{3-1}+x^{1-1}$$

Subtract 1 from 3.

$$21x^{2}+x^{1-1}$$

Subtract 1 from 1.

$$21x^{2}+x^{0}$$

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

$$21x^{2}+1$$

Evaluate

$$7x^{3}+x-27$$

Solution Steps

Combine 2x^{3} and 5x^{3} to get 7x^{3}.

$$7x^{3}+x-27$$