Solve 4x^3*7x^2=

$$4 x ^ { 3 } \cdot 7 x ^ { 2 } =$$

Evaluate

$$28x^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$4x^{5}\times 7$$

Multiply 4 and 7 to get 28.

$$28x^{5}$$

Differentiate w.r.t. x

$$140x^{4}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{5}\times 7)$$

Multiply 4 and 7 to get 28.

$$\frac{\mathrm{d}}{\mathrm{d}x}(28x^{5})$$

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

$$5\times 28x^{5-1}$$

Multiply 5 times 28.

$$140x^{5-1}$$

Subtract 1 from 5.

$$140x^{4}$$