Solve 27x-27x^4-1+9x

$$27 x - 27 x ^ { 4 } - 1 + 9 x$$

Differentiate w.r.t. x

$$36-108x^{3}$$

Steps Using Derivative Rule for Sum

Combine 27x and 9x to get 36x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(36x-27x^{4}-1)$$

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}.

$$36x^{1-1}+4\left(-27\right)x^{4-1}$$

Subtract 1 from 1.

$$36x^{0}+4\left(-27\right)x^{4-1}$$

Multiply 4 times -27.

$$36x^{0}-108x^{4-1}$$

Subtract 1 from 4.

$$36x^{0}-108x^{3}$$

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

$$36\times 1-108x^{3}$$

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

$$36-108x^{3}$$

Evaluate

$$-27x^{4}+36x-1$$

Solution Steps

Combine 27x and 9x to get 36x.

$$36x-27x^{4}-1$$