Solve (4(x)^(2))(7(x)^(5))((x)^(9)) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$(4 { x }^{ 2 } )(7 { x }^{ 5 } )( { x }^{ 9 } )$$

Evaluate

$28x^{16}$

Solution Steps

To multiply powers of the same base, add their exponents. Add $2$ and $5$ to get $7$.

$$4x^{7}\times 7x^{9}$$

To multiply powers of the same base, add their exponents. Add $7$ and $9$ to get $16$.

$$4x^{16}\times 7$$

Multiply $4$ and $7$ to get $28$.

$$28x^{16}$$

Differentiate w.r.t. x

$448x^{15}$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add $2$ and $5$ to get $7$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{7}\times 7x^{9})$$

To multiply powers of the same base, add their exponents. Add $7$ and $9$ to get $16$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{16}\times 7)$$

Multiply $4$ and $7$ to get $28$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(28x^{16})$$

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

$$16\times 28x^{16-1}$$

Multiply $16$ times $28$.

$$448x^{16-1}$$

Subtract $1$ from $16$.

$$448x^{15}$$