Solve ( iv ) x x | 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

$$x \times x ^ { 2 } \times x ^ { 3 } \times x ^ { 4 }$$

Evaluate

$x^{10}$

Solution Steps

To multiply powers of the same base, add their exponents. Add $1$ and $2$ to get $3$.

$$x^{3}x^{3}x^{4}$$

To multiply powers of the same base, add their exponents. Add $3$ and $3$ to get $6$.

$$x^{6}x^{4}$$

To multiply powers of the same base, add their exponents. Add $6$ and $4$ to get $10$.

$$x^{10}$$

Differentiate w.r.t. x

$10x^{9}$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add $1$ and $2$ to get $3$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}x^{3}x^{4})$$

To multiply powers of the same base, add their exponents. Add $3$ and $3$ to get $6$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{6}x^{4})$$

To multiply powers of the same base, add their exponents. Add $6$ and $4$ to get $10$.

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

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

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

Subtract $1$ from $10$.

$$10x^{9}$$