Solve -5y(-7y^3)

$$- 5 y ( - 7 y ^ { 3 } )$$

Evaluate

$$35y^{4}$$

Solution Steps

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

$$-5y^{4}\left(-7\right)$$

Multiply -5 and -7 to get 35.

$$35y^{4}$$

Differentiate w.r.t. y

$$140y^{3}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(-5y^{4}\left(-7\right))$$

Multiply -5 and -7 to get 35.

$$\frac{\mathrm{d}}{\mathrm{d}y}(35y^{4})$$

The derivative of ax^{n} is nax^{n-1}.

$$4\times 35y^{4-1}$$

Multiply 4 times 35.

$$140y^{4-1}$$

Subtract 1 from 4.

$$140y^{3}$$