Solve 7y*(-2y^3)+9y^4

$$7y \times (-2 { y }^{ 3 } )+9 { y }^{ 4 }$$

Evaluate

$$-5y^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$7y^{4}\left(-2\right)+9y^{4}$$

Multiply 7 and -2 to get -14.

$$-14y^{4}+9y^{4}$$

Combine -14y^{4} and 9y^{4} to get -5y^{4}.

$$-5y^{4}$$

Differentiate w.r.t. y

$$-20y^{3}$$

Steps Using Derivative Rule for Sum

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}.

$$\left(-14y^{3}\right)y^{1-1}+4\times 9y^{4-1}$$

Subtract 1 from 1.

$$\left(-14y^{3}\right)y^{0}+4\times 9y^{4-1}$$

Multiply 4 times 9.

$$\left(-14y^{3}\right)y^{0}+36y^{4-1}$$

Subtract 1 from 4.

$$\left(-14y^{3}\right)y^{0}+36y^{3}$$

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

$$\left(-14y^{3}\right)\times 1+36y^{3}$$

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

$$-14y^{3}+36y^{3}$$