Solve 5y^3-7+2y^3-y^2

$$5 y ^ { 3 } - 7 + 2 y ^ { 3 } - y ^ { 2 }$$

Differentiate w.r.t. y

$$y\left(21y-2\right)$$

Steps Using Derivative Rule for Sum

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(7y^{3}-7-y^{2})$$

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}.

$$3\times 7y^{3-1}+2\left(-1\right)y^{2-1}$$

Multiply 3 times 7.

$$21y^{3-1}+2\left(-1\right)y^{2-1}$$

Subtract 1 from 3.

$$21y^{2}+2\left(-1\right)y^{2-1}$$

Multiply 2 times -1.

$$21y^{2}-2y^{2-1}$$

Subtract 1 from 2.

$$21y^{2}-2y^{1}$$

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

$$21y^{2}-2y$$

Evaluate

$$7y^{3}-y^{2}-7$$

Solution Steps

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

$$7y^{3}-7-y^{2}$$