$y=2x^{5}$ $\dfrac{dy}{dx}=5\times 2x^{5-1}$ $\dfrac{dy}{dx}=10x^{4}$

$s=3t^{2}-t^{-1}$ $\dfrac{ds}{dt}=2\times 3t^{2-1}-(-1)\times t^{-1-1}$ $\dfrac{ds}{dt}=6t^{1}+t^{-2}$ $\dfrac{ds}{dt}=6t+\dfrac{1}{t^{2}}$ $\dfrac{d^{2}s}{dt^{2}}=1\times 6t^{1-1}+(-2)\times t^{-2-1}$ $\dfrac{d^{2}s}{dt^{2}}=6t^{0}-2t^{-3}$ $\dfrac{d^{2}s}{dt^{2}}=6-\dfrac{2}{t^{3}}$

$s=3t^{5}-5t^{-2}+11$ $\dfrac{ds}{dt}=5\times 3t^{5-1}-2\times 5t^{-2-1}-0$ $\dfrac{ds}{dt}=15t^{4}-10t^{-3}-0$ $\dfrac{ds}{dt}=15t^{4}-10t^{-3}$ $\dfrac{d^{2}s}{dt^{2}}=4\times 15t^{4-1}-(-3)\times 10t^{-3-1}$ $\dfrac{d^{2}s}{dt^{2}}=60t^{3}+30t^{-4}$ $\dfrac{d^{2}s}{dt^{2}}=60t^{3}+\dfrac{30}{t^{4Read more

$s=3t^{5}+7t-1$ $\dfrac{ds}{dt}=5\times 3t^{5-1}+1\times 7t^{1-1}-0$ $\dfrac{ds}{dt}=15t^{4}+7t^{0}-0$ $\dfrac{ds}{dt}=15t^{4}+7$ $\dfrac{d^{2}s}{dt^{2}}=4\times 15t^{4-1}+0$ $\dfrac{d^{2}s}{dt^{2}}=60t^{3}$

$s=4t^{3}-3t^{2}+t-5$ $\dfrac{ds}{dt}=3\times 4t^{3-1}-2\times 3t^{2-1}+1\times t^{1-1}-0$ $\dfrac{ds}{dt}=12t^{2}-6t+t^{0}-0$ $\dfrac{ds}{dt}=12t^{2}-6t+1$ $\dfrac{d^{2}s}{dt^{2}}=2\times 12t^{2-1}-1\times 6t^{1-1}+0$ $\dfrac{d^{2}s}{dt^{2}}=24t-6$