Solve 216y^6+12y^2-31^3

$$216 y ^ { 6 } + 12 y ^ { 2 } - 31 ^ { 3 }$$

Differentiate w.r.t. y

$$1296y^{5}+24y$$

Steps Using Derivative Rule for Sum

Calculate 31 to the power of 3 and get 29791.

$$\frac{\mathrm{d}}{\mathrm{d}y}(216y^{6}+12y^{2}-29791)$$

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}.

$$6\times 216y^{6-1}+2\times 12y^{2-1}$$

Multiply 6 times 216.

$$1296y^{6-1}+2\times 12y^{2-1}$$

Subtract 1 from 6.

$$1296y^{5}+2\times 12y^{2-1}$$

Multiply 2 times 12.

$$1296y^{5}+24y^{2-1}$$

Subtract 1 from 2.

$$1296y^{5}+24y^{1}$$

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

$$1296y^{5}+24y$$

Evaluate

$$216y^{6}+12y^{2}-29791$$

Solution Steps

Calculate 31 to the power of 3 and get 29791.

$$216y^{6}+12y^{2}-29791$$