Solve (8x ^ 2 * Z)/(10x * y ^ 2) | 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

$$\frac{8x^{2}Z}{10\ xy^{2}}$$

Differentiate w.r.t. x

$\frac{4Z}{5y^{2}}$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8Z}{10y^{2}}x^{2-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4Z}{5y^{2}}x^{1})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is $0$. The derivative of $ax^{n}$ is $nax^{n-1}$.

$$\frac{4Z}{5y^{2}}x^{1-1}$$

Do the arithmetic.

$$\frac{4Z}{5y^{2}}x^{0}$$

For any term $t$ except $0$, $t^{0}=1$.

$$\frac{4Z}{5y^{2}}\times 1$$

For any term $t$, $t\times 1=t$ and $1t=t$.

$$\frac{4Z}{5y^{2}}$$

Evaluate

$\frac{4Zx}{5y^{2}}$