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Find the derivative of $\frac{8-9t}{7}$ using the definition. Apply the definition of the derivative: $\displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$. The function $f(x)$ is the function we want to differentiate, which is $\frac{8-9t}{7}$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{\frac{8-9\left(t+h\right)}{7}-\frac{8-9t}{7}}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of (3t-7)/8=(8-9t)/7 using the definition. Find the derivative of \frac{8-9t}{7} using the definition. Apply the definition of the derivative: \displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}. The function f(x) is the function we want to differentiate, which is \frac{8-9t}{7}. Substituting f(x+h) and f(x) on the limit, we get. Combine \frac{8-9\left(t+h\right)}{7}-\frac{8-9t}{7} in a single fraction. Divide fractions \frac{\frac{8-9\left(t+h\right)-\left(8-9t\right)}{7}}{h} with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}. Multiply the single term -9 by each term of the polynomial \left(t+h\right).