Solve 10x^4^div5x

$$10 { x }^{ { 4 }^{ } } \div 5x$$

Evaluate

$$2x^{5}$$

Solution Steps

Calculate 4 to the power of 1 and get 4.

$$\frac{10x^{4}}{5}x$$

Divide 10x^{4} by 5 to get 2x^{4}.

$$2x^{4}x$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$2x^{5}$$

Differentiate w.r.t. x

$$10x^{4}$$

Steps Using Definition of a Derivative

Calculate 4 to the power of 1 and get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{10x^{4}}{5}x)$$

Divide 10x^{4} by 5 to get 2x^{4}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{4}x)$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{5})$$

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

$$5\times 2x^{5-1}$$

Multiply 5 times 2.

$$10x^{5-1}$$

Subtract 1 from 5.

$$10x^{4}$$